MTH 232

Section 14.1The Basics of Probability

Overview• Probability is the mathematics of uncertainty, in which

the likelihood that a chance event occurs is measured by a number between 0 (no chance of occurring) and 1 (must certainly occur). Students in grades 3 – 5 should begin to learn about this measurement.

• Previous to this, students will have begun to describe events as certain, likely, or impossible.

• Students should explore probability through experiments that have only a few outcomes (spinners and dice).

• They should use common fractions to express probabilities that are neither certain nor impossible.

Important Terms

• Experiment – something that takes place for which what will happen is uncertain

• Outcome – a possible result• Sample space – the set of all possible results• Favorable – what we would like to see happen• Unfavorable – what we would not like to see

happen

Examples

• For each experiment below, find the sample space:

1.Rolling a fair die2.Spinning the spinner shown below3.Tossing a coin4.Tossing two coins

Probability Ratio

• The probability that an event E occurs is the ratio of the number of ways that E can occur to the number of elements in the sample space S:

)()()Pr(SnEnE

Examples

• A penny, a nickel, and a dime are tossed. Find the probability of getting exactly 2 heads.

• A green die and a red die are tossed. Find the probability that the sum is:

a. 7b.Less than 4c. 13

More Examples

• A card is drawn from a standard deck of 52 playing cards. Find the probability that the card drawn is:

a. Blackb.The queen of diamondsc. A face card or a clubd.A face card and a club

Yet More Examples

• Recall the age data from our previous class. a. What is the probability that a randomly

selected person is legal drinking age in the state of Alabama?

b.What is the probability that a randomly selected person is over 30, given that the person is of legal drinking age?

Almost DoneOne M&M is chosen at random.a.What is the probability that it is orange?b.What is the probability that it is yellow, given that it is a primary color?c.What is the probability that is a primary color, given that it is yellow?d.What is the probability that it is purple?

Modified Homework

• 1 – 10, 14, 16, 32, 34, 35, 36