我有統計學問題~急><
1 a small grocery store has 10 cartons of milk, only 7 of which are fresh; the other 3 cartons are sour. if you are going to buy three cartons of milk that day at random, compute the probability of purchasing exactly one sour carton.
2 if p(a)=0.8, p(b)=0.5, and p(a∪b)=0.9 are a and b independent event? justify your answer.
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1.A small grocery store has 10 cartons of milk. Only 7 of which are fresh while the other 3 cartons are sour. If you are going to buy three cartons of milk that day at random, then compute the probability of purchasing exactly one sour carton.Solution:Take p=0.3 & q=0.7 for a binary distribution:(p+q)^3=p^3+3*p^2*q+3*p*q^2+q^3P(1 sour + 2 fresh)=3p*q^2=3*0.3*0.49=0.441........ans
2.If P(a)=0.8, P(b)=0.5, and P(a∪b)=0.9. Are a and b independent event? Justify your answer step by step.Proof: P(a∩b)=0 for independent!!P(a∩b)=P(a)+P(b)-P(a∪b)=0.8+0.5-0.9=0.4=\=0Thus it is dependent!!