Roll two fair dice. Each die has six faces. A. Let A be the event that either a 3 or 4 is rolled first followed by an odd number
. P(A) = .33 Round your answer to two decimal places. B. Let B be the event that the sum of the two dice is at most 7. P(B) = Round your answer to two decimal places. C. Are A and B mutually exclusive events? (Yes or No) yes D. Are A and B independent or dependent events? (Independent or Dependent)
1 answer:
Answer:
A. 0.16
B. 0.58
C. No
D. Dependent
Step-by-step explanation:
A.
The sampling space has 36 outcomes.
The event A has 6 outcomes (3,1), (3,3), (3,5), (4,1), (4,3),(4,5)
So P(A)= 6/36 = 0.16
B.
The table in the picture shows the 15 outcomes that are not allowed, so there are 36-15 = 21 possible outcomes for B and its probability is 21/36 = 0.58
C.
Are A and B mutually exclusive events?
No since their intersection is not empty, for example (3,1) belongs to both A and B
D.
In order for A and B to be independent, it must happen that
P(A∩B)=P(A)P(B)
A∩B={(3,1),(3,3),(4,1)} so P(A∩B) = 3/36
whereas
P(A)P(B) = (6/36)(21/36) = (1/6)(7/12)=7/72
So A and B are not independent.
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