probability set 1

8/16/2019 Probability Set 1

1/6

Probability Name :________________________ Class No: _______ Class: _____________

Write a short method and give all your answers in fractions

7. Three light bulbs are chosen at random from 12 bulbs of which 2 are

defective. Find the probability that

(a) none is defective

(b) exactly one is defective.

(a)

(b)

. We are given three bags as follows:

Bag contains 12 balls of which ! are red

Bag B contains 1" balls of which " are red.

Bag # contains $ balls of which 2 are red.

We select a bag at random and then draw a ball from it.

(a) What is the probability that the ball is red%

(b) &f a ball selected is red' what is the probability that it is drawn from

bag %

(a)

(b)

!. &n a class of !" students' 2" students failed (aths' 2) students failed

*hysics' and 1) students failed both sub+ects. student is selected at

random.

(a) &f he failed *hysics' find the probability that he failed in (aths.

(b) &f he failed (aths' find the probability that he failed in *hysics.

(c) Find the probability that he failed in (aths or *hysics' but not

both.

(a)

(b)

(c)

"#. Two people fire at a target at the same time. The probability that the first

person hits the target is 1,!' while the second person hits the target is 1,".

Find the probability that the target is hit.

"". Four students +oin the entrance exam of a university' the probabilities of

the students being accepted are-

1and

"

1'

1

2'

2)

- respectively. Find the

probability that at least one of them being accepted.


2/6

"$. Three players thrown a die one by one and the first to throw a /six0 wins.

Find the probability that

(a) the player who throws first wins'

(b) the player who throws next wins.

(a)

(b)

"%. n urn contains ! red balls and white balls. ball is drawn from the urn

and a ball of the other colour is then put into the urn. second ball is then

drawn from the urn.

(a) Find the probability that the second ball is red.

(b) &f both balls were of the same colour' what is the

probability that they were both red.

(a)

(b)

"&. man fires at a target with a probability of 1," hitting it. Find the

minimum number of fire in order that the probability of hitting the target is

at least !,".

"'. &n a competition' the chance for ohn gets the price is 1,- and gets the B

price is -,!. What is the chance for him to get at least a price assuming that

he cannot get both prices.

". bag contains 13 red balls and 1 white ball. 4 ta5es out a ball from the

bag at random and as5s 6. 6 tells 4 that it is a white ball. The chance 6 to

tell lie is 1,". What is the probability that the ball ta5en out from the bag is

a white ball%

"7. &n a television programme' a game is played. person who has been given

71)) plays under the following rules. t each toss of a fair coin' he bets

71)) dollars on either tail or head with e8ual return if he wins. The game

will be ended if

(") he has no money left'

($) the coin has been tossed five times.

&f he wins five times' an extra of 72))) will be given.

(a) Find the probability that the game will be ended at the - rd toss.

(b) Find the probability that he can win five times.

#alculate the amount of money he will get in this case.

(c) Find the probability that he has at least lost one time

in the game.

(a)

(b)

gb

(c)

". learner9driver is determined to pass the driving test eventually. The

probability that the learner9driver will pass the driving test on any one

(a)


3/6

occasion is 1,-. ach time the learner9driver ta5es the driving test' he has

to pay 7")).

Find the probability that the learner9driver will

(a) fail the test in both his first and second attempts'

(b) fail the test in his first three attempts but pass the test in his fourth

attempt'

(c) spend exactly 7-))) on driving test'

(d) spend more that 71))) on driving test.

(b)

(c)

(d)

Probability Name :________________________ Class No: _______ Class: ___________

Write a short method and give all your answers in fractions.

". Two balls are drawn from a bag containing - red' - green and ! blac5 balls. Find the probability that :

(a) both are red'

(b) one is green and one is blac5'

(c) both are of the same colour.

(a)1"1

32

1)- =×

(b)1"

!

3

-

1)

!

3

!

1)

-=×+×

(c)1"

!

3

-

1)

!

3

2

1)

-

3

2

1)

-=×+×+×

$. ;ne bag contains ! red balls and 2 blue balls< another bag contains - red

balls and " blue balls. ;ne ball is drawn from each bag' determine the

probability that:

(a) both are red'

(b) one is red and one is blue.

(a)!

1

$

-

!=×

(b)2!

1-

$

-

2

$

"

!=×+×

%. Four cards are drawn from a pac5 of "2 cards. =etermine the probability

that

(a) all are aces'

(b) they are ' >' ?'

(c) they are of the same suit.

(a)2)2"

1

!3

1

")

2

"1

-

"2

!=×××

(b)

2)2"

2"12-!

!3

!

")

!

"1

!

"2

!=×××××××

(c)

!1"

!!!

!3

1)

")

11

"1

12

"2

1-=××××

&. box contains " white cards and 1 red card. second box contains !

white cards. - cards are drawn from the first box and put into the second

box' and then 2 cards are drawn from the second box and put into the first.

=etermine the probability that the red card is still in the first box.

*@red from first box to second box and red from

second box to firstA

12

1-

1=×××=

*@white from first box to second box and white

from second box to firstA2

1

!

-

"

!

"=××=


4/6

*@red is in first boxA 1!

3

2

1

.

1=+

'. There are three bags. Bag contains 2 red coins and " white coins. Bag B

contains - red coins and ! white coins. Bag # contains ! red coins and -

white coins. bag is selected at random and a coin is drawn from it. Find

the probability that a red coin is drawn.

-

!

-

1

-

-

1

2

-

1=×+×+×

. There are 2 red balls and ! white balls in a box. Two balls are drawn from

the box. Find the probability that :

(a) both are red.

(b) the second ball is red when the first ball drawn is white.

(a)1"

1

"

1

2=×

(b)"

2

7. Three light bulbs are chosen at random from 12 bulbs of which 2 are

defective. Find the probability that

(a) none is defective

(b) exactly one is defective.

(a)11

1)

$

11

3

12

1)

=××

(b)22

3-

1)

3

11

1)

12

2=×××

. We are given three bags as follows:

Bag contains 12 balls of which ! are red

Bag B contains 1" balls of which " are red.

Bag # contains $ balls of which 2 are red.

We select a bag at random and then draw a ball from it.

(a) What is the probability that the ball is red%

(b) &f a ball selected is red' what is the probability that it is drawn from

bag %

(a) -

11

$

2

-

1

1"

"

-

1

12

!

-

1=×+×+×

(b) *@red ball is chosen in bag A

-

!

12

!

-

1=×

*@selected ball is drawn from bag A

11

!

-

11

-

!=

!. &n a class of !" students' 2" students failed (aths' 2) students failed

*hysics' and 1) students failed both sub+ects. student is selected at

random.

(a) &f he failed *hysics' find the probability that he failed in (aths.

(b) &f he failed (aths' find the probability that he failed in *hysics.

(c) Find the probability that he failed in (aths or *hysics' but not both.

(a)2

1

2)

1)

*hysicsfailedC

sub+ects bothfailedC==

(b)"

2

2"

1)

(athsfailedC

sub+ects bothfailedC==

(c)3

"

!"

1)22)2"

=×−+

"#. Two people fire at a target at the same time. The probability that the first

person hits the target is 1,!' while the second person hits the target is 1,".

Find the probability that the target is hit.

"

2

"

-1

"

11

!

111 =−=

−

−−


5/6

"". Four students +oin the entrance exam of a university' the probabilities of

the students being accepted are-

1and

"

1'

1

2'

2)

- respectively. Find the

probability that at least one of them being accepted.

"

-

-

2

"

!

1

1"

2)

11 =−

"$. Three players thrown a die one by one and the first to throw a /six0 wins.

Find the probability that

(a) the player who throws first wins'

(b) the player who throws next wins.

*@A D *@BA D *@#A 1'

@*-

2"AB@*

"A#@*A'@*

"AB@* ===

(a)31

-(b)

31

-)

"%. n urn contains ! red balls and white balls. ball is drawn from the urn

and a ball of the other colour is then put into the urn. second ball is then

drawn from the urn.

(a) Find the probability that the second ball is red.

(b) &f both balls were of the same colour' what is the

probability that they were both red.

(a)")

21

1)

"

1)

1)

-

1)

!=×+×

(b)

1)

"

1)

AW'W@*'

1))

12

1)

-

1)

!AE 'E @* ===

2

-)12

12=

+∴

"&. man fires at a target with a probability of 1," hitting it. Find the

minimum number of fire in order that the probability of hitting the target is

at least !,".

*@hitting target in one of the n firesA

1 *@not hitting target in all n firesA

"!

"

"

1

"

!

"

!

"

!1

nnn

≥

⇒≤

⇒≥

−

21.A!,"log@

"logn =≥ n $

"'. &n a competition' the chance for ohn gets the price is 1,- and gets the B

price is -,!. What is the chance for him to get at least a price assuming that

he cannot get both prices. 3

.

!

-

12

.

!

-

-

11

!

-

-

2

!

1

-

1

==×−

+

". bag contains 13 red balls and 1 white ball. 4 ta5es out a ball from the

bag at random and as5s 6. 6 tells 4 that it is a white ball. The chance 6 to

tell lie is 1,". What is the probability that the ball ta5en out from the bag is

a white ball%

*@6 tells 4 the ball is whiteA

1))

2-

"

!

2)

1

"

1

2)

13=×+×=

*@the ball is whiteA2-

!

1))

2-

1))

!

==

"7. &n a television programme' a game is played. person who has been given

71)) plays under the following rules. t each toss of a fair coin' he bets

71)) dollars on either tail or head with e8ual return if he wins. The game

will be ended if

(") he has no money left'

($) the coin has been tossed five times.

&f he wins five times' an extra of 72))) will be given.

(a)$

1

2

1 -

=

(b)-2

1

2

1 "

=

71)) D 7")) D 72))) 72))


6/6

(a) Find the probability that the game will be ended at the - rd toss.

(b) Find the probability that he can win five times.

#alculate the amount of money he will get in this case.

(c) Find the probability that he has at least lost one time

in the game.

(c)-2

-1

2

11

"

=

−

". learner9driver is determined to pass the driving test eventually. The

probability that the learner9driver will pass the driving test on any one

occasion is 1,-. ach time the learner9driver ta5es the driving test' he has

to pay 7")).

Find the probability that the learner9driver will

(a) fail the test in both his first and second attempts'

(b) fail the test in his first three attempts but pass the test in his fourth

attempt'

(c) spend exactly 7-))) on driving test'

(d) spend more that 71))) on driving test.

(a) 3

!

-

2

-

2

=

(b)$1

$

-

1

-

2

-

2

-

2=

(c).23

-2

-

1

-

2

-

2

-

2

-

2

-

2=

(d)3!

-2

-2 =

probability set 1

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