Exercise 4 Page 919

Isaiah has 3 quarters, 5 dimes, and 2 nickels in his pocket. We want to find the probability that he will randomly pull out two quarters in a row. The event of pulling out the first quarter affects the probability of pulling out the second one. This is because there is one fewer coin in Isaiah's pocket, and one fewer quarter to pull out. 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 P(A) of Isaiah randomly pulling out a quarter from his pocket. His pocket contains 10 coins in total, 3 of which are quarters. P(A)&=3/10 l←number of quarters ←number of coins P(B|A) is the probability of Isaiah pulling out a quarter from his pocket, given that the first coin he has pulled out is a quarter. Since he has already pulled a quarter out there are 9 coins remaining, two of which are quarters. P(B|A)&= 2/9 l←number ofremainingquarters ←number ofremainingcoins 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)= 3/10, P(B|A)= 2/9

P(AandB)= 3/10* 2/9

MultFrac

Multiply fractions

P(AandB)=6/90

ReduceFrac

a/b=.a /6./.b /6.

P(AandB)=1/15

CalcQuot

Calculate quotient

P(AandB)=0.066666...

RoundDec

Round to 2 decimal place(s)

P(AandB)≈0.07

The probability that Isaiah will randomly pull out two quarters in a row is 115, or approximately 0.07.