Question

A bag of skittles contains 18 yellow, 12 green, 20 red, 10 orange, and 14 purple

skittles. If one skittle is drawn at random, what is the

P( purple | color name with six letters )

Answer 1

1/3 for people who don’t want to read all of that

Answer 2

Answer: D) 1/3

===========================================================

Step-by-step explanation:

The vertical bar is a shorthand way of saying "Given".

Writing P(A | B) means "probability of A given B"

In this case, we are given that "color name with six letters", so we are 100% certain that whatever was picked has six letters in the color name. That rules out green (5 letters) and red (3 letters). We'll ignore these colors entirely.

Instead we focus on yellow, orange, and purple.

Add up the frequencies for these colors to get: 18 yellow + 10 orange + 14 purple = 42 total

Of that total, there are 14 purple, so....

14/42 = (1*14)/(3*14) = 1/3

represents the probability we're after.

There's a 1 in 3 chance of getting a purple skittle if we are told, or we know 100%, that whatever color we picked has 6 letters in the name.

Side note: 1/3 = 0.333 = 33.3% approximately.