4) We toss twice symmetric tetrahedral cube with sides: •, ••, •••, ••••. Let A - sum of dots is 4; B in second toss the number of dots \textgreater 3. Find $P(A)$, $P(B)$, $P(A \cap B)$, $P(A \cup B)$, $P(A')$, $P(B')$. Are A & B independent?
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There are 4 possible outcomes: 1+3, 2+2, 3+1, and 4+0. Each outcome has a probability of 1/6 * 1/6 = 1/36. Therefore, P(A) = 4/36 = 1/9. Show more…
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A pair of fair dice is tossed. Define the following events: A: {You will roll a 7.} (i.e., The sum of the dots on the up faces of the two dice is equal to 7.) B: {At least one of the two dice shows a 4.} a. Identify the sample points in the events A, B, A∪B, and A∩B. b. Find P(A), P(B), P(A∪B), P(A^c), and P(A∩B) by summing the probabilities of the appropriate sample points. c. Find P(A∪B) using the additive rule. Compare your answer to the one you obtained in part b. d. Are the events A and B mutually exclusive? Why?
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