1.A die is rolled. A=number is at least three. B=Number is odd. P(A/B)? 2.Rollin
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Question
1.A die is rolled. A=number is at least three. B=Number is odd. P(A/B)?
2.Rolling two dice. A=first number is 5. B= sum of two numbers is 7. Are A and B independent?
3.A book of 500 pages has 25 typos. Find the probability that the first page has no typo, 1 typo, or 2 typos.
4.Your team played 7 games. Outcomes are independent. Winning probability is 0.4. What is the probability that you win 4 games?
5. During 8 hours working day 10 phone calls come to your office. Find the probability that you will have no calls between 2pm and 3 pm.
Explanation / Answer
Solution:-
1.A die is rolled. A=number is at least three. B=Number is odd. P(A/B)?
A = {3,4,5,6} and B = {1,3,5}
P(A) = 4/6 = 0.667 and P(B) = 3/6 = 0.5
P(AIB) = P(AB) / P(B) = 0.333 / 0.5 = 0.667
2.Rolling two dice. A=first number is 5. B= sum of two numbers is 7. Are A and B independent?
A = {(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}
B = {(1,6),(2,5),(3,4),(5,2),(6,1)}
No, the given two events are not independent. Because when two events are said to be independent of each other, what this means is that the probability that one event occurs in no way affects the probability of the other event occurring.
3. A book of 500 pages has 25 typos. Find the probability that the first page has no typo, 1 typo, or 2 typos.
P(typo) = 25/500 = 0.05
P(no typo) = 1 - 0.05 = 0.95
P(the first page has no typo, 1 typo, or 2 typos) = 0.95 + 0.05 + 0.0025 = 1.0025
4.Your team played 7 games. Outcomes are independent. Winning probability is 0.4. What is the probability that you win 4 games?
P(winning) =0.4
P(Lossing) = 0.6
P(winning 4 games) = 0.4 * 4 = 0.16
5. During 8 hours working day 10 phone calls come to your office. Find the probability that you will have no calls between 2pm and 3 pm.
Working hours = 8,
P(phone call every hour) = 0.8
Poisson Probability : P(X = 0) = 0.449328964117222 or 0.449
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