Question

Your teacher is giving away candy from a bag. The bag contains 5 Reese's Peanut

Butter Cups, 4 Snickers, 3 Sour Patch, & 6 Skittles. Find the probability that you and
your friend choose Snickers. Find P(Snickers n Snickers).

Answer 1

P(Snickers n Snickers) =
`(2)/(51)`

Explanation:

Given

Bag of candy

5 Reese's Peanut Butter Cups,

4 Snickers

3 Sour Patch

6 Skittles

Required

Calculate P(Snickers n Snickers)

To solve this question, it'll be assumed that you and your friend selected snickers at a consecutive time.

First, we need to calculate the total number of candy

Total = 5 + 4 + 3 + 6

Total = 18 candies

P(Snickers n Snickers) means P(Snickers and Snickers);

i.e. the probability of selecting snicker twice

Number of snickers = 4;

So, the probability of you selecting a snicker first is
`(4)/(18)`

This is gotten by dividing number of snickers by total candies.

At this point, there are 4 - 1 snickers left and there are 18 - 1 candies left;

So, the probability of your friend selecting a snicker is
`(4 - 1)/(18 - 1)`.

So, P(Snickers n Snickers) =
`(4)/(18)` *
`(4 - 1)/(18 - 1)`

P(Snickers n Snickers) =
`(4)/(18)` *
`(3)/(17)`

P(Snickers n Snickers) =
`(2)/(9)` *
`(3)/(17)`

P(Snickers n Snickers) =
`(2)/(3)` *
`(1)/(17)`

P(Snickers n Snickers) =
`(2)/(51)`

Hence, the probability of you and your friend choosing snickers is
`(2)/(51)`