Nhan is getting dressed. he considers two different shirts, three pairs of pants, and three pairs of shoes. he chooses one of each of the articles at randon. what is the probability that he will wear his jeans but not his sneakers?

Question Continuation

Shirt: Collared, T-shirt

Pants: Khakis, Jeans, Shorts

Shoes: Sneakers, Flip-Flops, Sandals

The probability that he will wear his jeans but not his sneakers = 2/9

Step-by-step explanation:

Given

Shirt: Collared, T-shirt

Pants: Khakis, Jeans, Shorts

Shoes: Sneakers, Flip-Flops, Sandals

First, we need to list out the sample space.

The sample space is the list of all possible dress combination.

With assumption that he must pick one from each category, the sample space represented by S is as follows;

S = { Collared/Khakis/Sneakers, Collared/Khakis/Flip-flops, Collared/Khakis/Sandals, Collared/Jeans/Sneakers, Collared/Jeans/Flip-flops, Collared/Jeans/Sandals,

Collared/Shorts/Sneakers, Collared/Shorts/Flip-flops, Collared/Shorts/Sandals,

T-shirt/Khakis/Sneakers, T-shirt/Khakis/Flip-flops, T-shirt/Khakis/Sandals, T-shirt/Jeans/Sneakers, T-shirt/Jeans/Flip-flops, T-shirt/Jeans/Sandals,

T-shirt/Shorts/Sneakers, T-shirt/Shorts/Flip-flops, T-shirt/Shorts/Sandals}

Total Possible Outcome = 18

Let J represent the outcome that he wears Jean but not sneakers

J = {Collared/Jeans/Flip-flops, Collared/Jeans/Sandals,

T-shirt/Jeans/Flip-flops, T-shirt/Jeans/Sandals,

}

Total Possible Outcome of Jean without sneakers = 4

The probability that he will wear his jeans but not his sneakers is given by (Total Possible Outcome of Jean without sneakers) ÷ (Total Possible Outcome)

The probability that he will wear his jeans but not his sneakers = 4/18

The probability that he will wear his jeans but not his sneakers = 2/9