Exercise 1 Page 817

Are the events dependent or independent?

2/25

Practice makes perfect

Rico is selling the following candy.

8 milk chocolate bars
6 candy bars
5 dark chocolate bars
6 peanut butter bars

Marissa selects two candy bars from these randomly. We want to know the probability that Marissa buys a milk chocolate bar, followed by a candy bar. When Marissa buys one bar, the total number of bars decreases. Because of this, the probability for the second bar is changed. Therefore, these events are dependent. P( milk chocolate and candy ) = P(milk chocolate) * P(candy |milk chocolate) To find the probability that Marissa buys a milk chocolate first, we need to know how many bars there are in total. Let's do it! 8+ 6+ 5+ 6 = 25 Now we can find the probability that Marissa buys a milk chocolate.

P(milk chocolate) = Number of milk chocolate bars/Number of bars

SubstituteValues

Substitute values

P(milk chocolate) = 8/25

Since Marissa already bought one bar, Rico has 24 bars left. Let's find the probability that Marissa buys a candy bar after she bought a milk chocolate.

P(candy |milk chocolate) = Number of candy bars/Number of bars left

SubstituteValues

Substitute values

P(candy |milk chocolate) = 6/24

ReduceFrac

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

P(candy |milk chocolate) = 1/4

Now we can find the probability that Marissa buys a milk chocolate bar, followed by a candy bar.

P( milk chocolate and candy ) = P(milk chocolate) * P(candy |milk chocolate)

SubstituteValues

Substitute values

P( milk chocolate and candy ) = 8/25 * 1/4