Question

Consider a standard deck of 52 cards. You select one card at random and do not replace it. You shuffle the deck and then pick another card. If you are trying to find the probability that you pick a Red card first (denoted by R) and then a King card (denoted by K), which of the following probability statements is applicable for finding the probability?

a. P(R )P(K|R)
b. n(R AND K)/n(S)
c. P(R|K )P(K|R)
d. P(R )+P(K)-P(R n K)

Answer 1

a. P(R )P(K|R)

Explanation:

The two cards are picked one after the other without replacement.

First card =Red (R)

Second Card=King(K)

The probability we want to find is the conditional Probability of picking a King card GIVEN that a Red Card(R) was already picked.

That is: P(K|R)

For two mutually exclusive events,

P(K|R) = P(K∩R)÷P(R)

Cross Multiplying

P(K∩R)=P(R)P(K|R)