A pair of fair dice is cast. Let E denote the event that the number falling uppermost in the first die is 5 and let F denote the event that the sum of the numbers falling uppermost is 8. Compute . Are E and F dependent events?
A) , yes
B) , no
C) , no
D) , yes

Question

A pair of fair dice is cast. Let E denote the event that the number falling uppermost in the first die is 5 and let F denote the event that the sum of the numbers falling uppermost is 8. Compute  . Are E and F dependent events?
A) , yes 
B) , no 
C) , no 
D) , yes

Quizplus · Accepted Answer

We need to find the probability of both events E and F occurring:
P(E and F) = P(E) x P(F|E)

Probability of E = number 5 on first die = 1/6
Probability of F given that E has occurred: 
There are 5 options for the number on the first die, but only one of these (3) will give a sum of 8 with the other die. Therefore, P(F|E) = 1/36
P(E and F) = (1/6) x (1/36) = 1/216

To check for independence:
P(E) = 1/6
P(F) = 5/36
P(E and F) = 1/216

If E and F are independent events, then P(E and F) = P(E) x P(F). However, we can see above that P(E and F) is not equal to P(E) x P(F), so E and F are dependent events.

Therefore, the correct answer is D: 11eab448_e7e3_eb38_acdb_2f7a20263be8_TB6027_11, yes.

A Pair of Fair Dice Is Cast