SOLUTION: 2. An experiment consist of rolling a pair of dice. Event E1 is the event that 7 occurs, I.e., the sum on the dice is 7. Event E2 is the event that an odd number occurs on die 1. F

Algebra ->  Probability-and-statistics -> SOLUTION: 2. An experiment consist of rolling a pair of dice. Event E1 is the event that 7 occurs, I.e., the sum on the dice is 7. Event E2 is the event that an odd number occurs on die 1. F      Log On


   

Question 1118623: 2. An experiment consist of rolling a pair of dice. Event E1 is the event that 7 occurs, I.e., the sum on the dice is 7. Event E2 is the event that an odd number occurs on die 1. Find
a. Pr {E1}
b. Pr{E2}
c. Pr{E1∩E2}
d. Pr{E1UE2}
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
a) Pr{E1} = 6/36 = 1/6 (there are 6 ways to roll a 7 out of 36 possible outcomes)

b) Pr{E2} = 3/6 = 1/2 (there are 3 ways to roll an odd number out of 6 possible outcomes)

c) Pr{E1 ∩ E2} = 3/36 = 1/12 (3 out of 36 possible outcomes fall in the intersection, or, one can multiply the results of (a) and (b))

d) Pr{E1 U E2 } = 21/36 = 7/12 (this is the set of elements that comprise E1, E2, or both E1 & E2. We can count them: E1: Die1={1, 3, 5} has 18 outcomes, and E2 {sum of Die1 and Die2 = 7} has 6 outcomes, but we've over counted by 3 outcomes (where Die1 is odd and Die1+Die2 = 7). One can also compute (a) + (b) - (c) = 6/36+18/36 - 3/36 = 21/36 = 7/12.