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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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.

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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?