e 12-26. Prove the following :(i) If P(A | B) 2 P(A) then P(B | A) 2 P(B).(ii) If P(B|A) = P(B | A), then A and B are independent events.PO

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Answered: e 12-26. Prove the following: (i) If…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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3 2 1. Given that P(4)=, P(A/ B)= and P(A/B)=. find : P(ANB) P(B) P(AUB) (а) (i) (ii) (iii) (b) Determine whether the events A and B are : (i) (ii) Mutually exclusive Independent (c) Given that P(A)=0.64 , P(B)=0.36 and P(BnA)= 0.25. Find : (i) P(AOB) (ii) P(AUB) (iii) P(BnA)
1 Let A and B be events with P(A) = P(B) = " and P(AB) =. What is P[(ANB)U(BnA)]? None of these O 9/10 4/5 O 19/30
1. Let A and B be independent events with P (A) = 0.7 and P (B) = 0.2. Compute: (a) P (A∩B) (b) P (A∪B) (c) P (A∪B′).
Let B₁..... B, be independent events. Show P(UB)=1-1-PC P(B₁)). iml
a) Show that for any three events A, B, and C, the probability that at least one of them occurs is P(A) + P(B) + P(C) - P(An B)- P(ANC) - P(BNC) + P(An BnC). b) Given A and B are independent events, with P(A) = 0.50 and P(B) = 0.30. Find P(ANB) c) About 52% of the residents of Capricorn municipality are happy and 48% of the residents are not happy with the delivery service. A recent study showed that 75% of happy residents and 25% of the unhappy residents are in favour of keeping the mayor of the municipality. If resident is randomly selected from the municipality residents is found to favour the motion. What is the probability that this person is happy with the delivery service?
If P (not B) = 0.55, P (A ∪ B) = 0.75, and A and B are independent events, then find p (A)
94l 6 PA:19 H.W_3 Let A and B be events with P(A) = 1. P(B) = 1 and P(AUB) . Find (i) P(A ) B), (ii) P(B|A), (ii P(AnB), (iv) P(A | B). 147
4. Let A und B be two events such that: P(A)=0.48. P(B)=0.67 and P(AnB)=0.22 Then P(AUB) = a) 0.55 b) 0.93 c) 0.26 d) 0.87
Show that for any events A and B, P (A ∩ B) ∪ (A ∩ B) = P(A) + P(B) − 2P(A ∩ B)
3 a) The events A and B are such that P(A) =0.3, P(B'| A) =0.8 and P(B| A')=0.4. Find P(AOB) and P(AUB). Hence, state with reason whether A and B are independent events. b) A box contains 5 balls labelled 1, 2, 3, 4 and 5. A player draws a ball from the box randomly. If the number on the ball drawn is 2, 3 or 4, the players score is that number. If the number on the ball is 1 or 5, the player can draw a second ball without replacing the first ball, and his score is the sum of the numbers on the two balls. The events A and B are defined as follows A: The score of a player is 4, 5, 6 or 7. B: A player draws two balls from the box. Find P(A), P(B), P(ANB) and P(AUB).
94 AA:19 EA s E7 H.W 3 Let A and B be eventa with P(A) = 1, P(B) = and P(AUB) =1 Find (i) P(A| B), (ii) P(B |4), (ii) P(ANB), (iv) P(A | B). زين الدين عبد الرحمن حسين مرحلة 2/نظم المعلوم. . . 12:47 äcluI 21.02.09

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e 12-26. Prove the following: (i) If P(A | B) 2 P(A) then P(B | A) 2 P(B). (ii) If P(B\A) = P(B| A), then A and B are independent events.