Exercise 5 Page 787

The event of selecting the first animal cracker affects the probability of selecting the second animal cracker. This is because there is one fewer animal cracker from which we select. Therefore, the events are dependent.

Probability of Dependent Events

If two events A and B are dependent, then the probability that A and B will occur is P(AandB)=P(A)* P(B|A)

Let's start by calculating the probability of selecting a tiger cracker. In the given bag of animal crackers, there are 20 crackers and we have 3 tiger crackers. P(A)&=3/20 l←tiger crackers ←all animals Here, P(B|A) is the probability of selecting another tiger cracker, given that the first selected cracker is a tiger cracker. Because we already picked one cracker, there are 19 crackers left and out of these we have 2 tiger ones. P(B|A)&= 2/19 l←remainingtiger crackers ←remainingcrackers Finally, according to the formula, to calculate P(AandB) we have to multiply P(A) and P(B|A).

P(AandB)=P(A)* P(B|A)

SubstituteII

P(A)= 3/20, P(B|A)= 2/19

P(AandB)= 3/20* 2/19

MultFrac

Multiply fractions

P(AandB)=6/380

ReduceFrac

a/b=.a /2./.b /2.

P(AandB)=3/190