Which of the following represents Pr[X = 11] ?

Question

A wallet contains two 1-dollar bills, three 5-dollar bills, and one 10-dollar bill. Two of the bills are randomly selected from the wallet, without replacement, and the random variable X is defined to be X = total value (in dollars) of the two bills selected from the wallet. Which of the following represents Pr[X = 11] ?

Answer 1

There are two ways to add up to $11.

a) Pick a $1 and a $10

b) Pick a $10 and a $1

The probability for (a) is (2/6)(1/5) = 2/30 = 1/15

The probability for (b) is (1/6)(2/5) = 2/30 = 1/15

Pr[X=11] = 1/15 + 1/15 = 2/15

Answer 2

2 ones

3 fives

1 ten

6 total

pick two without replacement

Pr(one & ten) =(1/3)(1/5= 1/15 total value = $11

Pr(x=11) = 1/15