Probability and Odds

Algebra Seminar2012-2013

When the weather channel predicts that the chance of rain for the next day is 70%, it is telling us that the likelihood for this precipitation to occur is 7 chances out of 10.

What is Probability?

• Probability is a numerical measure indicating the chance or likelihood for a particular event to occur.

* It is usually expressed as a ratio namely by a fraction, decimal, or percent.

Example: When we toss a coin in the

air, it is equally likely that it will land heads up as tails up. Therefore, the chance that this coin will land heads up is one out of two, or 1/2.

The set of all the possible outcomes of a given experiment is called the sample space.

Probability of an event =

Dice A typical dice has 6 sides. Each side

contains a number from 1-6. If you roll a die, what is the

probability of getting:

1. A 4?

2. An odd number?

3. A number less that 3?

4. A number more than 6?

We said that the probability of rolling a 4 is 1/6.

If we roll a die 30 times, how many times am I likely to get a 4?

1. A 2, in 60 rolls.

2. An odd number, in 100 rolls.

3. A number less than 3, in 300 rolls.

4. A number greater than 6, in 1000 rolls.

Suppose the 8 letters of the words HOT COCOA are written on cards, then shuffled. If a card is chosen at random, the probability that it will contain the letter 0 is _____. What is the probability that it will contain:

The letter C?A vowel?A letter in the word CHOCOLATE?

Probability is often expressed in terms of “odds”.

Example There are 12 colored marbles in

a bag, and 3 of them are blue. What are the odds for drawing a blue marble from the bag?

ExampleWhat are the odds that you will

win the prize if you hold 50 raffle tickets of the 1500 tickets sold at a charity affair?

Spinners A spinner has a circle with twelve

numbers each numbered 1-12. What are the odds that the pointer stops on the first spin by a number divisible by 4?

Numbers divisible by 4 include: 4,8, and 12.