Question

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 spade. ​(b) Compute the probability of randomly selecting a diamond or spade or heart. ​(c) Compute the probability of randomly selecting a four or club.

Answer 1

Answer:

Step-by-step explanation:

a: there will be 13 diamond cards, and 13 spade cards, 26 total, so your probability will be $frac (13+13){52}= \frac 12$.  If you think about it, you are trying to get a card from half the deck.

b: again, there will be 13 diamonds, 13 spades, and 13 hearts, $frac (13+13+13){52}= \frac 34$. You'll be good as long as you don't draw clubs, which are 1/4 of your deck, so it's 3/4 left!

c: The favorable outcomes are 13 (the clubs) and 3 remaining fours, your probability is $\frac{13+3}{52}=\frac4{13}$

Answer 2

We want to find the probabilities of drawing specific cards for 52 card deck.

• a) p = 1/2
• b) p = 3/4
• c) p = 4/13

We start by assuming that all the cards have the same probability of being drawn, then.

a) probability of randomly selecting a diamond or spade.

This will be equal to the quotient between the total number of diamonds and spades (13 of each, so 26 in total) and the total number of cards in the deck (52).

p = 26/52 = 1/2

b) probability of randomly selecting a diamond or spade or heart.

Similar to before, this will be equal to the quotient between the total number of diamonds, spades and hears (39 in total) and the total number of cards in the deck:

p = 39/52 = 3/4

c) probability of randomly selecting a four or club.

In a deck there are 4 fours and 13 clubs (and one of these clubs is one of the fours, so we need to not count it twice). Then we have 4 + 13 - 1 = 16 cards that meet the criteria.

Here the probability will be:

p = 16/52 = 4/13

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