Q3. A balls are randomly selected without replacement. box in a certain supply r
ID: 2923292 • Letter: Q
Question
Q3. A balls are randomly selected without replacement. box in a certain supply room contains 15 green balls and 8 red balls. Suppose that four (a) What is the probability that exactly two of the selected balls are red? b) What is the probability that at least one of the selected balls are green? (c) Suppose that there are now 15 green balls and 8 red balls and 4 yellow balls. What is the probability that exactly one of the selected balls are red and exactly one of the selected balls are yellow? (d) Suppose now that balls are to be selected one by one until a red ball is found. What is the probability that it is necessary to examine at least eight balls?Explanation / Answer
A) P(selecting 2 red ball) = 8C2 * 15C2 / 23C4 = 28*105/8855 = 0.332
B) P(at least one green ball) = 1 - P(none of the ball is green)
= 1 - 8C4/23C4
= 1 - 70/8855
= 0.9921
C) P(one red and one yellow) = 8C1 * 4C1 * 15C2 / 27C4
= 8*4*105/17550
= 0.1915
D) here calculation is made with 15 green and 8 red balls
P(examine at least 8 balls) = 1 - [P(examine 1*ball( + P(examine 2 balls) +.... + P(examine 7balls)
= 1 - [8/23 + 15/23 * 8/22 + 15/23 * 14/22 * 8/21 +... + 15/23 * 14/22 * 13/21 * 12/20 * 11/19 * 10/18 * 8/17]
= 1 - 0.9738
= 0.0262
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