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

Section: Chapter Questions

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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B: If we throw piece of dice (two) times, the event(A) represent appearance of two sides are similar, the event of( B) represent appearance of two sides are similar, their total score is 8, the event of( C) represent appearance of two sides, their total score is 5, show the sample space of this practice, then find two of the following? 1. The probability of appearance of two sides are similar, their total score is (8). ." 2. The probability of appearance of two sides are similar, or their total score is ( 8)... 3. The probability of appearance of two sides, their total score is (5) or (8) ....
11 The probability of a man hitting a target is How many times 4 must he fire so that the probability of his hitting the target atleast once is greater than
18. The probability of winning a game in a casino is 0.4. A player plays 5 games in a row and each game is independent from another. What is the probability of winning all 5 games?
8 For this problem, assume there are 3 grey females, 4 grey males, 2 white females, and 3 white males. As in the book, the biologist selects two mice randomly. (1) What is the probability of selecting two males given that both are grey? (2) What is the probability of selecting 1 mouse of each gender given that both are grey?
17. Two dice are rolled. Find the probability that: (a) The sum of the numbers is 8. (b) The sum of the numbers is less than 13. (c) The sum of the numbers is more than 8. (d) The sum is less than 4.
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
What is the answer of this 3 questions?
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.
(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?