Question

10 point A box contains three defective and seven non defective chips. Three chips are drawn randomly without replacement one after the other. Let X be the # of defective chips. Using hyper geometric model construct the probability distribution of X and show that it fulfills the two conditions of probability distribution. Also find E(X) 1 Add file Page 2 Back Submit LALAR

Answer 1

conditions :

1. Total number of items (population) is fixed.

this conditions is satisfied as no new chips are added

2. Sample size (number of trials) is a portion of the population. Probability of success changes after each trial.

satisfied, because after each draw replacement is not done so probability changes

N C. P(x)= N-sCn-s when S = successes from population S = successes from sample N = population size 11 = sample size

P(X) = ( 7C(3-x) * 3Cx ) / 10C3

[ nCr = n!/(r! * (n-r)!) ]

E(x) = sample size * (no. of defective / total no.)

= 3 * (3/10)

E(x) = 0.9

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