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- If P(E)= 0.2, P(F) = 0.3, and E and F are independent events, find P(E and F). 1) 0.06 2) 0.08 3) 0.1 4) 0.12 5) 0.5 6) 0.9 7) 0 8) 1Let A denote the event that the next item checked out at a college library is a math book, and let B be the event that the next item checked out is a history book (assume there are no math history books). Suppose that P(A) = .40 and P(B) = .50.• Compute P(A′) =• Compute P(A ∪ B) =• Compute P(A′ ∩ B′) =1. Let A and B be random events. Show that if AC B then P(A) < P(B).
- Q. 2 Suppose the following three boxes are given: Box A contains 3 red and 5 white mobile phones Box B contains red and 1 white mobile phones Box C contains 2 red and 3 white mobile phones A box is selected at random, and a mobile phone is randomly drawn from the box. If the mobile phone is red, find the probability that it came from the box A.1.39 A pair of events A and B cannot be simultaneously mutually exclusive and independent. Prove that if P(A) > 0 and P(B) > 0, then: (a) If A and B are mutually exclusive, they cannot be independent. (b) If A and B are independent, they cannot be mutually exclusive.2 dice, one green and one black, are rolled once. Which of the following events are independent? 1. E= A 2 is rolled on the green die, F= A sum of 7 is rolled on both dice. 2. E= A 3 is rolled on the green die, F= A 5 is rolled on the black die. 3. E= A sum of 3 is rolled on both dice, F= A 4 is rolled on the black die. 4. E= A 2 is rolled on the green die, F= A sum of 8 is rolled on both dice.
- Which one of the following statements is False (not true)? Events A and B are independent if and only if P(A and B) = P(A) x P(B). Events A and B are independent if and only if P(A) = P(A given B). O(A) x O(not A) = 1 Events A and B are independent if and only if A and B are mutually exclusive; that is disjoint. If events A and B are mutually exclusive then, P (A or B) = P(A) + P(B).A signal will fail to get through a network when the following combination of events (R n R2) U R is true. All three events (R. R2, and R) are statisticaly independent and each has a probability of 0.2. Determine the probability of no signal getting through, i.e. Determine: P ((R n Ra)U R) Select one: O a. 0.352 O b. 0.240 O c. 0.200 O d. 0.0601. Suppose that E and F are independent events such that Pr[E] = .3 and Pr[F] = .4.(a) Find Pr[E ∩ F].(b) Using your answer to the previous question, fill out the Venn diagram for E and F:(c) Find the following probabilities:i. Pr[E ∩ F Compliment]ii. Pr[E Compliment ∩ F]iii. Pr[E Compliment ∩ F Compliment]
- 2. Page 34, 1.4.14*. Each of three persons fires one shot at a target. Let Ck denote the event that the target is hit by person k, k = 1, 2, 3. If C1, C2, C3, are independent and if P(C1) = P(C2) = 0.8, and P(C3) = 0.9, compute the probability that (a) all of them hit the target; (b) exactly one hits the target; (c) no one hits the target; (d) at least one hits the target.Q no 2 part b
