A magic bag contains 8 raspberries, 6 watermelons, and 7 bananas. 5 pieces of fruits are taken out from the magic bag randomly without replacement. Find the probability that
(a) 3 raspberries and 2 watermelons are taken
(b) the 5 pieces of fruits taken are all bananas
(c) all of the 5 fruits taken are the same kind
(d) the 5 pieces taken contain at least 4 raspberries.
a)
"P=\\frac{C^3_{8}\\cdot C^2_{6}}{C^5_{26}}=\\frac{8!6!}{3!5!2!4!}\\frac{5!21!}{26!}=0.0128"
b)
"P=\\frac{ C^5_{7}}{C^5_{26}}=\\frac{7!}{5!2!}\\frac{5!21!}{26!}=0.0003"
c)
"P=\\frac{C^5_8}{C^5_{26}}+\\frac{C^5_6}{C^5_{26}}+\\frac{C^5_7}{C^5_{26}}+\\frac{1}{C^5_{26}}=\\frac{8!}{5!3!}\\frac{5!21!}{26!}+6\\frac{5!21!}{26!}+\\frac{7!}{5!2!}\\frac{5!21!}{26!}+\\frac{5!21!}{26!}="
"=0.0009+0.00009+0.0003+0.00001=0.0013"
d)
"P=\\frac{C^4_{8}\\cdot C^1_{22}}{C^5_{26}}+\\frac{C^5_{8}}{C^5_{26}}=22\\frac{8!}{4!4!}\\frac{5!21!}{26!}+\\frac{8!}{5!3!}\\frac{5!21!}{26!}=0.0234+0.0009=0.0243"
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