Question

Two marbles are drawn in succession from the box containing 10 red, 30 white, 20 blue, and 15 orange marbles. replacement being made after each drawing. Find the probability that is: (a) both are white (b) the first is red and the second is white (c) neither is orange (d) they are either red or white or both ( red and white ) (e) the second is not blue (f) the first is orange (g) at least one is blue (h) at most one is red (i) the first is white but the second is not (j) only one is red

Answer 1

(a) The probability that both marbles are white is $(30/85) * (30/85) = (\frac{1}{17})^2.$

(b) The probability that the first is red and the second is white is (10/85) * (30/85) = $(\frac{2}{17})^2$=0.013

(c) The probability that neither is orange is (1 - 15/85) * (1 - 15/85) = (70/85) * (70/85)=0.67

(d) The probability that they are either red or white or both is (10/85) + (30/85) + (10/85 * 30/85) = (12/17) + (36/289)=0.83

(e) The probability that the second is not blue is 1 - (20/85) = 65/85=0.76

(f) The probability that the first is orange is 15/85=0.17

(g) The probability that at least one is blue is 1 - (65/85 * 64/84) = 51/85=0.6

(h) The probability that at most one is red is (10/85) + (74/85 * 73/84) = (10/85) + (54/289)=0.30

(i) The probability that the first is white but the second is not is (30/85) * (55/84)=0.23

(j) The probability that only one is red is (10/85 * 74/84) + (75/85 * 10/84) = (7/17) + (5/17)=0.70

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