Question

a standard deck of cards contains 52 cards. one card is selected from the deck. (a) compute the probability of randomly selecting a six or king. (b) compute the probability of randomly selecting a six or king or nine. (c) compute the probability of randomly selecting a king or spade. click the icon to view a deck of cards (a) p(six or king) = (type an integer or a decimal rounded to three decimal places as needed.)

Explanation:

Step1: Find number of sixes and kings

There are 4 sixes and 4 kings in a deck of 52 cards.

Step2: Use addition - rule for non - overlapping events

The formula for $P(A\ or\ B)$ when $A$ and $B$ are non - overlapping events is $P(A\ or\ B)=P(A)+P(B)$. Here, $A$ is the event of selecting a six and $B$ is the event of selecting a king. So $P(\text{six or king})=\frac{4 + 4}{52}=\frac{8}{52}\approx0.154$.

Step1: Find number of sixes, kings and nines

There are 4 sixes, 4 kings and 4 nines in a deck of 52 cards.

Step2: Use addition - rule for non - overlapping events

Since the events of selecting a six, a king and a nine are non - overlapping, $P(\text{six or king or nine})=\frac{4+4 + 4}{52}=\frac{12}{52}\approx0.231$.

Step1: Identify number of kings, spades and king of spades

There are 4 kings, 13 spades and 1 king of spades in a deck of 52 cards.

Step2: Use addition - rule for overlapping events

The formula for $P(A\ or\ B)$ when $A$ and $B$ are overlapping events is $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$. Here, $A$ is the event of selecting a king and $B$ is the event of selecting a spade. So $P(\text{king or spade})=\frac{4+13 - 1}{52}=\frac{16}{52}\approx0.308$.

Answer:

0.154

For part (b) and (c), we will continue in the same step - by - step manner:

(b)