Problem 2 Finding the Probability of Independent Events

Picnic At a picnic there are 10 diet drinks and 5 regular drinks. There are also 8 bags of fat-free chips and 12 bags of regular chips. If you grab a drink and a bag of chips without looking, what is the probability that you get a diet drink and fat-free chips?

A and B are independent. Picking a drink has no effect on picking the chips.

P ( A  and  B ) = P ( A ) ⋅ P ( B )   = number of diet drinks total number of drinks ⋅ number of bags of fat-free chips total number of bags of chips   = 10 15 ⋅ 8 20 = 4 15 ≈ 0.267 , or  26.7 % table with 3 rows and 2 columns , row1 column 1 , p open eh , and b close , column 2 equals p open eh close dot p open b close , row2 column 1 , , column 2 equals . fraction numberofdietdrinks , over totalnumberofdrinks end fraction . dot . fraction numberofbagsoffatminusfreechips , over totalnumberofbagsofchips end fraction , row3 column 1 , , column 2 equals , 10 over 15 , dot , 8 twentieths , equals , 4 fifteenths , almost equal to , 0.267 , comma or , 26.7 , percent , end table

The probability that you get a diet drink and fat-free chips is about 26.7%.

✓ Got It?

2. In Problem 2, what is the probability that you get a regular drink and regular chips?

Problem 3 Mutually Exclusive Events

You roll a standard number cube. Are the events mutually exclusive? Explain.

1. rolling a 2 and a 3

   You cannot roll a 2 and 3 at the same time. The events are mutually exclusive.

2. rolling an even number and a multiple of 3

   You can roll a 6—an even number and a multiple of 3—at the same time. The events are not mutually exclusive.

✓ Got It?

3. You roll a standard number cube. Are the events mutually exclusive? Explain.
   1. rolling an even number and rolling a prime number
   2. rolling an even number and rolling a number less than 2

Take Note Key Concept: Probability of A or B

P ( A  or  B ) = P ( A ) + P ( B ) − P ( A  and  B ) p open eh , or b close equals p open eh close plus p open b close minus p open eh , and b close

If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B).