Question

Mikayla buys a bag of cookies that contains 8 chocolate chip cookies, 4 peanut butter cookies, 8 sugar cookies and 9 oatmeal cookies. What is the probability that Mikayla randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects a sugar cookie?

Answer 1

To calculate the total probability of picking a chocolate chip cookie first and a sugar cookie second, we multiply the probabilities of each individual event, which results in a combined probability of 16/203.

Step-by-step explanation:

Initially, Mikayla has a total of 29 cookies in her bag (8 chocolate chip, 4 peanut butter, 8 sugar, and 9 oatmeal cookies). The probability of selecting a chocolate chip cookie first is the number of chocolate chip cookies divided by the total number of cookies, which is 8/29. After eating the chocolate chip cookie, there are now 28 cookies left in the bag with 8 sugar cookies among them.

So, the probability of then picking a sugar cookie is 8/28, or reduced to 2/7. To find the combined probability of both events, we multiply the probabilities of each individual event: (8/29) × (2/7).

The calculations give us the following:

1. Probability of picking a chocolate chip cookie first: 8/29.
2. Probability of picking a sugar cookie second, after eating a chocolate chip cookie: 2/7.
3. Total combined probability: (8/29) × (2/7) = 16/203.

Answer 2

Probability = 0.0788

Step-by-step explanation:

Mikayla buys a bag containing,

Sugar cookies = 8

Oatmeal cookies = 9

Chocolate cookies = 8

Peanut cookies = 4

Total number of cookies in the bag = 8 + 9 + 8 + 4 = 29

Probability that Mikayla randomly selects a chocolate chip cookie

=
`\frac{\text{total number of chocolate cookies}}{\text{Number of cookies in the bag}}`

=
`(8)/(29)`

Now number of cookies left in the bag = 29 - 1 = 28

She eats it then randomly selects another cookie.

Probability that the selected cookie will be a sugar cookie

=
`\frac{\text{total number of sugar cookies}}{\text{Number of cookies left in the bag}}`

=
`(8)/(28)`

=
`(2)/(7)`

Now probability of occurrence of both the events =
`(8)/(29)* (2)/(7)`

=
`(16)/(203)`

= 0.0788