Questions: A standard deck of cards contains 52 cards. One card is selected from the deck.
(a) Compute the probability of randomly selecting a diamond or club.
(b) Compute the probability of randomly selecting a diamond or club or heart.
(c) Compute the probability of randomly selecting an eight or diamond.
(a) P(diamond or club) =
(Type an integer or a decimal rounded to three decimal places as needed.)
(b) P(diamond or club or heart) =
(Type an integer or a decimal rounded to three decimal places as needed.)
(c) P(eight or diamond) =
(Type an integer or a decimal rounded to three decimal places as needed.)
Transcript text: A standard deck of cards contains 52 cards. One card is selected from the deck.
(a) Compute the probability of randomly selecting a diamond or club.
(b) Compute the probability of randomly selecting a diamond or club or heart.
(c) Compute the probability of randomly selecting an eight or diamond.
(a) P (diamond or club) $=$ $\square$
(Type an integer or a decimal rounded to three decimal places as needed.)
(b) P (diamond or club or heart) $=$ $\square$
(Type an integer or a decimal rounded to three decimal places as needed.)
(c) $P($ eight or diamond $)=$ $\square$
(Type an integer or a decimal rounded to three decimal places as needed.)
Solution
Solution Steps
Step 1: Compute the probability of randomly selecting a diamond or club
A standard deck has 52 cards.
There are 13 diamonds and 13 clubs in the deck.
The total number of favorable outcomes is \( 13 + 13 = 26 \).
The probability \( P(\text{diamond or club}) \) is calculated as:
\[
P(\text{diamond or club}) = \frac{26}{52} = 0.500
\]
Step 2: Compute the probability of randomly selecting a diamond or club or heart
There are 13 diamonds, 13 clubs, and 13 hearts in the deck.
The total number of favorable outcomes is \( 13 + 13 + 13 = 39 \).
The probability \( P(\text{diamond or club or heart}) \) is calculated as:
\[
P(\text{diamond or club or heart}) = \frac{39}{52} = 0.750
\]
Step 3: Compute the probability of randomly selecting an eight or diamond
There are 4 eights in the deck (one for each suit).
There are 13 diamonds in the deck.
However, the eight of diamonds is counted in both groups, so we subtract 1 to avoid double-counting.
The total number of favorable outcomes is \( 4 + 13 - 1 = 16 \).
The probability \( P(\text{eight or diamond}) \) is calculated as:
\[
P(\text{eight or diamond}) = \frac{16}{52} \approx 0.308
\]