25-42 ■ Probability These exercises involve probability.

Selecting Cards Three cards are randomly selected from a standard 52 -card deck, one at a time, with each card replaced in the deck before the next one is picked. Find the probability of each event.

(a) All three cards are kings.

(b) Exactly two of the cards are jacks.

(c) None of the cards is a face card.

(d) At least one of the cards is a face card.

(a)

To find:

The probability that all three cards are kings if three cards are randomly selected from a standard 52-card deck, one at a time, with each card replaced in the deck before the next one is picked.

Approach:

Write the formula to find the probability

P(E)=(n(E)n(S))×(n(E)n(S))×(n(E)n(S)) …(1)

Here, P(E) The probability that all three cards are kings if three cards are randomly selected from a standard 52-card deck, one at a time, with each card replaced in the deck before the next one is picked, n(E) is the number of possible cases, n(S) is the number of total cases.

Calculation:

Substitute 4 for n(E) and 52 for n(S) in equation (1),

(b)

To find:

The probability that exactly two of the cards are jacks if three cards are randomly selected from a standard 52-card deck, one at a time, with each card replaced in the deck before the next one is picked.

(c)

To find:

The probability that none of the cards is a face card if three cards are randomly selected from a standard 52-card deck, one at a time, with each card replaced in the deck before the next one is picked.

(d)

To find:

The probability that at least one of the cards is a face card if three cards are randomly selected from a standard 52-card deck, one at a time, with each card replaced in the deck before the next one is picked.