Question

A card stack contains white and black cards. Two cards are drawn randomly without replacement. The probability of selecting a white and then a black card is x. The probability of selecting a white card in the first draw is y. You have to find the probability of drawing a black card, given that the first card drawn was white

Answer 1

Answer:

Probability of drawing a black card, given that the first card drawn was white = x/y

Step-by-step explanation:

It is given that probability of selecting a white and then a black card is x and also probability of selecting a white card in the first draw is y.

Now Let A = Probability of drawing a black card

and Let B = Probability of first card drawn be white

Now we have P(B) = y and P(A $\bigcap$ B) = x

We know that P(A/B) = $\frac{P(A\bigcap B)}{P(B)}$  where $\bigcap$ represent intersection

So Probability(drawing a black card, given that the first card drawn was white) = P(A/B) = (Probability of selecting a black card and then a white card)  

                             / (Probability of first card drawn be white)

                        = $\frac{x}{y}$  

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