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.)

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.)
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Solution

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

Final Answer

(a) \( \boxed{0.500} \)
(b) \( \boxed{0.750} \)
(c) \( \boxed{0.308} \)

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