Two boxes are labeled I and II. Box I contains 4 black balls and 6 white balls.
ID: 3022560 • Letter: T
Question
Two boxes are labeled I and II. Box I contains 4 black balls and 6 white balls. Box II contains 2 black balls and 8 white balls. A player randomly draws one ball from each box (so that a total of 2 balls arc obtained). What is the probability of obtaining at least one black ball What is the probability of obtaining exactly one black ball What is the probability of obtaining no black ball What is the probability of obtaining 2 black balls Given that at least one black ball is obtained, what is the probability that exactly one black ball is obtained Given that at least one black ball is obtained, what is the probability that the bail from box I is black Given that exactly one black hall is obtained, what is the probability that the ball from box I is black Let X be the number of black balls obtained by the player. Find the probability mass function of X. Find the mean and variance of X.Explanation / Answer
Let 1,2 = the number of the box chosen
B, W = wlack/white
1.
P(at least one black) = 1 - P(no black)
=1 - P(white at 1) P(white at 2)
=1 - (6/10)*(8/10)
= 13/25 or 0.52 [ANSWER]
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2.
P(exatly 1 black) = P(black at 1) P(white at 2) + P(white at 1) P(black at 2)
= (4/10)*(8/10) + (6/10)*(2/10)
= 0.44 [ANSWER]
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3.
P(no black) = P(white at 1) P(white at 2)
= (6/10)*(8/10)
= 0.48 [ANSWER]
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4.
P(2 black) = P(black at 1) P(black at 2)
= (4/10)*(2/10)
= 0.08 [ANSWER]
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