Drawing a Card Four cards are drawn from a deck without

Problem 13E

Drawing a Card, Four cards are drawn from a deck without replacement. Find these probabilities.

a. All are kings.

b. All are diamonds.

c. All are red cards.

                                                            Step by step solution

Step 1 of 3

(a)

Let, P(K) denote the probability that all four cards are king drawn from a deck of cards without replacement. Outcome of each draw is independent of other, before or after, we can apply multiplication rule of probability and rule of empirical probability, ie;

Formula for Empirical Probability:

Given a frequency distribution, the probability of an event being in a given class is

P(E) =

This probability is called empirical probability and is based on observation

Multiplication Rule 1:

When two events are independent, the probability of both occurring is,

P(A and B)  = P(A) . P(B)

Applying the above equations:

There are 4 kings of different suits in a deck of cards.

P(K) = P (King in 1st draw). P (King in 2nd draw). P (King in 3rd draw). P (King in 4th draw)

P(K) =