Thread: HEP ME>>>> Prob Dist

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7. A drawer contains four red socks and five blue socks.
(a) Three socks are drawn one at a time and then put back before the next
selection. Determine the probability that
(i) exactly two red socks are selected
(ii) at least two red socks are selected
(b) Repeat part (a) without replacement

Originally Posted by wikji

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7. A drawer contains four red socks and five blue socks.
(a) Three socks are drawn one at a time and then put back before the next
selection. Determine the probability that
(i) exactly two red socks are selected
(ii) at least two red socks are selected

When sampling with replacement you have a binomial distribution for the
number of sucesses, so here the number of redsocks has binomial distribution
B(3,4/9)

so for (i) you want b(2,3,4/9), and for (ii) b(2,3,4/9)+b(3,3,4/9)

(b) Repeat part (a) without replacement

Here the probability of two red socks in three choices is

p(n=2)=p(rrb)+p(rbr)+p(brr)

where rrb denotes the first two socks are red and the third is blue, etc.

So:

p(n=2)=(4/9)(3/8)(5/7)+(4/9)(5/8)(3/7)+(5/9)(4/8)(3/7)

and:

p(n>=2)=p(n=2)+p(n=3)

RonL