Day 5 – Intro to probability (Section 11.5 Day 1)

Random Experiment: Experiments that do not yield the same results, no matter how carefully they are repeated under the same conditions. (i.e. rolling dice, flipping a coin, etc) Outcome: A possible result from the experiment (i.e. each way in which 2 dice can show up) Outcomes are EQUALLY LIKELY results of a random experiment. Sample Space: The set outcomes (i.e. the sum of 2 dice totaling to 6) PROBABILITY:

Ex. 1: Suppose that 2 dice are rolled, a black one and a white one. Find: a) P(sum of 8) b) P(is at least 8) c) P(sum is 13) d) P(is less than 13) e) P(the black die is a 3 or the white die is a 5) f) P(the black die is a 3 and the white die is a 5)

the sample space of rolling 2 dice is given (Lower right) – but let’s try another way and check with our sample space. (1-2)- you roll one die 1. What is the probability of rolling a 3? 2. P(3 or a 6)?

(3-4)- you roll tw0 dice 3. P(3 and a 6)? 4. P(3 then a 6)? you roll one die 5. P(at least a 3)?

# 1 2 3 4 5 6

1 2 3 4 5

6

You can also use pictures, tree diagrams and/or venn diagrams to help

Ex 3: When 2 coins are tossed, what is the probability that: Tree:

a. P(two tails)

b. P(one tails then one heads)

c. P(one tails and one heads)

Now let’s flip 3 coins:

d. P (one heads then two tails) e. P (one head and two tails)

16. The spinners below have an equal chance of landing

on any one number.

Find the probability of spinning: a. an even number on Spinner A b. Spinners A and B are spun.

Calculate P(two even numbers). c. Spinners A and C are spun. d. All three spinners are spun. Calculate P(an even and an odd). Calculate P(all evens). e. All three spinners are spun. f. All three spinners are spun. Calculate P(at least one odd). Calculate P(1 odd and 2 evens).