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.)

Solution Steps

• 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: $$P(\text{diamond or club}) = \frac{26}{52} = 0.500$$

• 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: $$P(\text{diamond or club or heart}) = \frac{39}{52} = 0.750$$

• 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: $$P(\text{eight or diamond}) = \frac{16}{52} \approx 0.308$$

Final Answer