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Probability - select 10 cards WITH replacement

 
 
TB54321
 
Reply Tue 18 Feb, 2014 10:54 pm
I tried to attempt some but do not now if I am doing them right...

Select 10 cards from a standard 52-card deck, with replacement, so that independence is achieved. Compute the following binomial probabilities:

(a) at least four of the cards are clubs.
Attempt: .14599+.05839+.1622+.003+.3.862+2.861+9.536=

(b) exactly two of the cards are clubs.
Attempt = .2815

(c) at most five cards are clubs.

(d) at least one card is a club.
Attempt: (4/52)(4/52)(4/52)(4/52)(4/52)(4/52)(4/52)(4/52)(4/52)(4/52) =

(e) exactly three of the cards are 5’s
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markr
 
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Reply Tue 18 Feb, 2014 11:17 pm
@TB54321,
The probability that exactly N cards are clubs is:
C(10,N) * (1/4)^N * (3/4)^(10-N)
which is:
the number of ways that N of the 10 can be selected as clubs
times the probability that those N are clubs
times the probability that the others are all not clubs

C(n,r) = n! / (r! * (n-r)!)

You can compute the results for 0-10 and sum appropriately.
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