Mathematics, 04.07.2020 14:01 hemaam8

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 a three or club.

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Answer from: addisonrausch

To solve the questions we must know the concept of Probability.

The probability of randomly selecting a diamond or club is 50%.The probability of randomly selecting a diamond or a club or heart is 75%The probability of randomly selecting a diamond or a club or heart is 30.77%.What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

Explanations

(a) Compute the probability of randomly selecting a diamond or club.

Probability( Diamond or club)

The number of diamond cards = 13

The number of club cards = 13

The total number of diamond and club cards = 26

$\rm{Probability(Diamond\ or\ club)=\dfrac{Number\ of\ diamond\ or\ club\ cards}{Total\ Number\ of\ cards}$

$\rm{Probability(Diamond\ or\ club)=\dfrac{26}{52}=\dfrac{1}{2} = 0.5 = 50\%$

(b) Compute the probability of randomly selecting a diamond or club or heart.

Probability( Diamond or club or heart)

The number of diamond cards = 13

The number of club cards = 13

The number of heart cards = 13

The total number of diamond, heart, and club cards = 39

$\rm{Probability(Diamond\ or\ club\ or\ hearts)=\dfrac{Number\ of\ diamond\ or\ club\ or\ hearts\ cards}{Total\ Number\ of\ cards}$

$\rm{Probability(Diamond\ or\ club\ or\ hearts)=\dfrac{39}{52}=\dfrac{3}{4} = 0.75 = 75\%$

Probability( three or club)

The number of three cards = 4

The number of club cards = 13

The total number of diamond and club cards = 13+4 - 1 =16

we reduced a card because card three of the club is calculated twice.

$\rm{Probability(three\ or\ club)=\dfrac{Number\ of\ three\ or\ club\ cards}{Total\ Number\ of\ cards}$

$\rm{Probability(three\ or\ club)=\dfrac{16}{52}=0.3077 = 30.77\%$

Learn more about Probability:

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Answer from: dontcare95

Ok, in a deck of 52 cards we have:

13 clubs, 13 diamonds, 13 hearts, and 13 spades.

For this problem, we assume that the probability of selecting a card at random is the same for all the cards, so each card has a probability of 1/52 of being selected.

then the probability of drawing a given outcome, is equal to the number of times that the outcome appears in the deck divided the number of cards.

a) probability of randomly selecting a diamond or club.

in the 52 cards deck, we have 13 diamonds and 13 clubs, so the probability of drawing a diamond or a club is equal to:

P = (13 + 13)/52 = 26/52 = 0.5

b) Compute the probability of randomly selecting a diamond or club or heart.

Same reasoning as before, here we have 13 + 13 + 13 = 39 possible options, so the probability is:

p = 39/52 = 0.75.

c) Compute the probability of randomly selecting a three or club.

we have 13 club cards, and in the deck, each number appears 4 times, so we have 4 cards with a number 3 on them.

But one of those 3's is also a club card, so we already counted it in the 13 club cards, then the number of possible options here is:

13 + 4 - 1 = 13 +3 = 16

then the probability is: