Gifty Addae

Gifty Addae

Answered question

2022-07-30

Answer & Explanation

Jazz Frenia

Jazz Frenia

Skilled2023-05-29Added 106 answers

(a) To compute the probability of randomly selecting a diamond or spade, we need to determine the number of favorable outcomes (diamonds and spades) and divide it by the total number of possible outcomes (all cards in the deck).
In a standard deck of 52 cards, there are 13 cards of each suit (diamonds, spades, hearts, and clubs). Therefore, there are 13 diamond cards and 13 spade cards.
The total number of favorable outcomes is 13 (diamonds) + 13 (spades) = 26.
The total number of possible outcomes is 52 (total cards in the deck).
The probability of randomly selecting a diamond or spade is given by:
Probability=Number of favorable outcomesTotal number of possible outcomes=2652=12=0.5
(b) To compute the probability of randomly selecting a diamond, spade, or heart, we include the number of favorable outcomes for each of these suits.
In a standard deck of 52 cards, there are 13 cards of each suit.
The total number of favorable outcomes is 13 (diamonds) + 13 (spades) + 13 (hearts) = 39.
The total number of possible outcomes is still 52 (total cards in the deck).
The probability of randomly selecting a diamond, spade, or heart is:
Probability=Number of favorable outcomesTotal number of possible outcomes=3952=0.75
(c) To compute the probability of randomly selecting a five or diamond, we need to determine the number of favorable outcomes (five cards and diamond cards) and divide it by the total number of possible outcomes (all cards in the deck).
In a standard deck of 52 cards, there are 4 fives (one for each suit) and 13 diamond cards.
The total number of favorable outcomes is 4 (fives) + 13 (diamonds) = 17.
The total number of possible outcomes is still 52 (total cards in the deck).
The probability of randomly selecting a five or diamond is:
Probability=Number of favorable outcomesTotal number of possible outcomes=17520.327

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