# What is the probability that a red card was picked first given that the second card is white.When two cards are picked from a pile containing 48 red and white cards, the probabillity of picking a...

What is the probability that a red card was picked first given that the second card is white.

When two cards are picked from a pile containing 48 red and white cards, the probabillity of picking a red card followed by a white card is 0.35. The probability that a red card is picked is 0.75.

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### 1 Answer

The pile of cards contains 48 red and white cards. The probability that a red card is picked is 0.75, this gives the probability that a white card is picked as 1 - 0.75 = 0.25.

The probability that a red card is picked followed by a white card is given as 0.35.

The probability of a red card being picked first given that the second is a white has to be determined.

Let A be the event that a white card is picked. P(A) = 0.25. B is the event that a red card is picked P(B) = 0.75.

The probability that a red card is picked followed by a white card is 0.35.

=> P(A and B) = 0.35

The probability that a red card was picked first given that the second cars is white is P(B|A) = P(A and B)/P(A)

=> 0.35/0.25 = 1.4

But the probability of an event cannot be greater than 1.

There is an error in the problem, the probability that a red card is picked followed by a white card is not 0.35 but 0.75*12/47 = 0.1914

**The probability that a red card is picked followed by a white card is not 0.35 but 0.1914**

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