Question

Let a bowl contain 10 chips of the same size and shape. One and only one of those chips is res. Continue to draw chips from the bowl, one at the time and at random without replacemeent, until the red chip is drawn. Let x be the number of trials needed to draw a red chip. a) Find the probability mass function of x. b) Compute Pr[x<=4].

Answer 1

Let a bowl contain 10 chips of the same size and shape. One and only one of those chips is res. Continue to draw chips from the bowl, one at the time and at random without replacemeent, until the red chip is drawn. Let x be the number of trials needed to draw a red chip. a) Find the probability mass function of x. b) Compute Pr[x<=4]. -------------------------------------- If x = 1, P(x=1) = 1/10 If x = 2, P(x=2) = (9/10)(1/9) = 1/10 If x = 3, p(x=3) = (9/10)(8/9)(1/8) = 1/10 If x = 4, p(x=4) = (9/10)(8/9)(7/8)(1/7) = 1/10 ----------------- P(x<=4) = 4/10 = 2/5 ============================== Cheers, Stan H.