بسم الله الرحمن الرحيم

هذه بعض التمارين في الاحتمالات Probabilities اتمنى من اخواني واخواتي في هذا الصرررح أن يساعدوني في إيجاد الحل لها لاني محتاج لحلولها .

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as soon as possible

.
In answering a question on a multiple choice a student either knows the answer or she guesses. Let p be the probability that she knows the answer and 1-p the probability that she will be correct with probability that a student knew the answer to a question given that she answered in correctly is
mp/(1+( m-1)p) .

2-
Suppose each of three persons tosses a coin. If the outcome of the tosses differs from the other outcomes, then the game ends. If not, then the persons start over and re-toss their coins. Assuming fair, What is the probability that the game will end with the first round of tosses?. If all three coins are biased and have a probability 1/4 of landing heads, then what is the probability that the game will end at the first round.

3.
. Store A,B and C have 50. 75 and 100 employees, and respectively 50, 60 and 70 percent of these are women. Resignations are equally likely among all employees, regardless of sex. One employee resigns and this is a women. What is the probability that she works in store C ?

4.
An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn c additional balls of the same color are put in with in. Now suppose that we draw anther ball. Show that the probability that the first ball drawn was black given that the second ball drawn was red is
b/(b+r+c)

5.
. A coin is to be tossed as many times as is necessary to turn up one head. Thus the sample space Ω = {H, TH , TTH , TTTH, TTTTH,…} Let he probability measure P (.) assign to these element the respective probabilities 1/(2 ) , 1/(4 ) , 1/(8 ) , 1/(16 ) and so forth. If A_1 = {H, TH , TTH , TTTH, TTTTH} and A_2 = { TTTTH, TTTTTH}, compute P( A1), p(A2), P(A1∩A2) and P(A1∪A2)

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