Alicia's mom keeps a variety of small chocolate bars on a table for guests.

Question

There are 3 Twix bars, 3 Milky Ways, and 3 Snickers bars to choose from. What is the probability that her next guest will randomly choose a Twix bar and a Snickers?

A: 33%

B: 8%

C: 12.5%

D: 11%

Answer 1

There are a total of 9 candy bars.

A single random choice means that it is equally-likely that any one of the 9 bars will be chosen. One way to implement "random" choice is to use a blindfold or equivalent so the choice must be made without information about the candy brand.

A single choice has 3/9 (that is, (3 successful events) / (number of total events) ) = 1/3 for each brand.

However, the second random choice is a "success" only if the first choice was already successful (note: "and"). There are 3 Snickers after a Twix bar is selected (or vice versa), so, the probability is (3/8) of the (1/3) previous successes. That is (3/8)*(1/3) = 0.125 = 12.5%

Answer 2

The probability of selecting a Twix is ³/₉

The probability of next selecting a Snickers is ³/₈ (since there are now only 8 to choose from instead of 9)

When we have an AND probability, we multiply the probabilities

So the probability of selecting a Twix and then a Snickers is ³/₉ * ³/₈