Question

Jeremy is randomly selecting an outfit to celebrate Probability Day at his school. He can choose from a green (G) or purple (P) shirt, denim (D) or khaki (K) pants, argyle (A) or crew (C) socks, and boots (B), flip-flops (F) or sneakers (S). What is the probability that Jeremy will select an outfit that includes flip-flops (F) and argyle (A) socks?

Answer 1

a

Explanation:

Answer 2

16.67% probability that Jeremy will select an outfit that includes flip-flops (F) and argyle (A) socks

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes. To find the number of outcomes, we use the permutations formula.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

Desired outcomes:

One shirt, from a set of 2.

One pant, from a set of 2.

Argyle socks.

Flip flops.

So

`D = P_{{2,1)}*P_{{2,1)} = 4`

Total outcomes:

One shirt, from a set of 2.

One pant, from a set of 2.

One sock, from a set of 2.

One footwear, from a set of 3.

So

`T = P_{{2,1)}*P_{{2,1)}*P_{{2,1)}*P_{{3,1)} = 24`

Probability:

`p = (D)/(T) = (4)/(24) = 0.1667`

16.67% probability that Jeremy will select an outfit that includes flip-flops (F) and argyle (A) socks