They contain all 4 aces. One card is drawn from 52. Find the probability that it

Question

They contain all 4 aces. One card is drawn from 52. Find the probability that it is an ace given that it is not a king. A box contains 10 light bulbs, 2 of which are defective. Suppose that 3 bulbs are selected in a row, without replacement. Find the probability that All 3 bulbs arc good. At least one is defective. Exactly one bulb is defective, Choose one card from 52 and consider the events E: The card is a heart F: The card is an ace. Are E and F independent? Choose one card from 52 and consider the events The card is a heart F: The card is a picture card. Are E and F independent?

Explanation / Answer

5. a. P(X=r)

=nCr(p)^r(q)^n-r=3C3(0.2)^3(0.8)^0=0.008

b. P(at least 1 is defective)=P(non-defective)^C

=1-(0.8)^3=0.488

c. P(x=1)=3C1(0.8)^1(0.2)^2=0.096

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