Four six-sided dice have their sides painted red and white. On two dice, three s
ID: 2922381 • Letter: F
Question
Four six-sided dice have their sides painted red and white. On two dice, three sides are painted red, and three sides are painted white. On the third die. 1 side is painted red, and 5 sides are painted white. On the fourth die. 5 sides are painted red and 1 side is painted white If one of the four dice is selected at random and rolled, what is the probability that a red side shows on iop? (a) b) If two of the four dice are selected at random and rolled, what is the probability that the two sides showing on top have the same color? If you perform the experiment of part (b), and observe that both dice show red on top, what is the probability that both of the two dice that were selected have three red sides, and three white sides? (c)Explanation / Answer
(a) Probability that white side shows on top on the first two dice = 1/2.
Probability that white side shows up on the third die = 5/6.
Probability that red side shows up on the fourth die = 1/6.
=> Probability that all four dice show red = 1/2 * 5/6 * 1/6 = 5/72.
Probability that a red side shows up on top = 1 - 5/72 = 65/72 = 0.9028.
(b) If the two dice are the first two, probability that same color appears on top = 1/2.
If one dice is from the first two and the other dice from the last two, probability that the two dice show the same color = (1/6 + 1/6 + 1/6 + 5/6 + 5/6 + 5/6) / 6 = 1/2.
Note that the above can be done in 4 ways.
If the two are dice are the last two dice, the probability is = (1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 5/6) / 6 = 5/18.
=> Probability that both dice that come up are of the same color = (1/2 + 4*1/2 + 5/18) / 6 = 0.4630.
(c) Probability that the selected dice were from the first two
= 4*1/2 / (1/2 + 4*1/2 + 5/18)
= 0.72.
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