4. Suppose a fair die is rolled 3 times. Let A; be the event that the ith roll is asix for i = 1, 2, 3.(a) What is P(A₁ U A₂)?(b) What is P(A₁ U A2 U A3)?(c) What is the probability of at least one 6 among the three rolls?

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Answered: 4. Suppose a fair die is rolled 3…

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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If A and B are complements, then which of the following is true about the probability of B based on the probability of A? 1) P(B)=P(A)+1 2) P(B)=1-P(A) 3) P(B)=1/P(A) 4) P(B)=P(A)-1
Suppose there are 6 red balls and 4 white balls in a urn.(1) event A={First draw is a white ball}, what is P(A), probability of A?(2) Now assume we do picking balls one by one without replacement. event B={Second draw is a white ball}, what is P(B), probability of B? (3) Are A and B independent? Justify your answer. please explain and do all the steps fully!
3. Two coins are tossed 700 times, and the results are Two heads: 205 times One head: 325 times No head: 170 times Find the probability of each event to occur? 4. If P(A)-7/13, P(B)-9/13 and P(ANB)-4/13, evaluate P(A/B)? 5. Two dice are rolled, find the probability that the sum of the number of both the dice is: A.Equal to 2 B.Equal to 5 C.Less than 12 6. Let X be the number of Tell in four tosses of a fair coin a) Construct the Probability mass function (pf) of X. b) Find the mean number of Tell and the variance c) Find P(0 2. (i)Determine the corresponding p.d.f. (f(x)). (ii) Determine the constant c. 8. If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value 9.Find the probability of getting at least 5 times head-on tossing an unbiased coin for 6 times by using the binomial distribution
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The yellow and green dice are tossed together. If A is the event that a 2 is shown on the yellow die and B is the event that 3 is shown on the green die, thena) determine P(A), P(B)b) Find the probability of getting a 2 on the yellow die and a 4 on the green.
f a baseball player has a batting average of 0.255, what is the probability that the player will get the following number of hits in the next four times at bat? (A) Exactly 2 hits (B) At least 2 hits
(2) A box contains 4 red balls, 3 green balls and 4 black balls. Three balls are drawn at random without replacement, and then the probability that the balls have same color is (а) 1/36 (b) 17/33 (c) 15/36 (d) 5/36 (e) 15/33 (f) None of these
1. If a die is rolled, find out the following: (i) The probability of getting an even number (ii) The probability of getting a 4 2. If two dice are rolled, then find out the following: (i) The probability that the sum is equal to 9 (ii) The probability that the sum is equal to 7 If a card is drawn at random from a pack of 52 cards, then find out the following: (1) P(Ace or Red) (ii) P(Non Black or Ace) 3. 4. A Jar contains 3 red, 4 green and 3 blue balls. If two balls are chosen at random from the Jar, Find out the following: (i) The probability that they are red or green. (ii) The probability that they are blue or red. 5. If three coins are tossed, then find out the following- (i) Probability of getting two tails (ii) Probability of getting three heads 6. Of the cars on a used car lot, 70% have CD player (CD) and 30% have air conditioning (AC). 10% of the cars have both. (i) What is the probability that a car has 'No AC', given that it has 'CD'? (ii) What is the probability that a car…
(3) A box contains 6 red balls, 7 green balls and 5 black balls. Three balls are drawn at random without replacement, and then the probability that the balls have same color is (а) 34/136 (b) 17/133 (c) 15/136 (d) 10/136 (e) None of these

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4. Suppose a fair die is rolled 3 times. Let A; be the event that the ith roll is a six for i = 1, 2, 3. (a) What is P(A₁ U A₂)? (b) What is P(A₁ U A2 U A3)? (c) What is the probability of at least one 6 among the three rolls?