Respuesta :
Answer:
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:
p = 16/52 = 0.31
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.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
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
[tex]\rm{Probability(Diamond\ or\ club)=\dfrac{Number\ of\ diamond\ or\ club\ cards}{Total\ Number\ of\ cards}[/tex]
[tex]\rm{Probability(Diamond\ or\ club)=\dfrac{26}{52}=\dfrac{1}{2} = 0.5 = 50\%[/tex]
(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
[tex]\rm{Probability(Diamond\ or\ club\ or\ hearts)=\dfrac{Number\ of\ diamond\ or\ club\ or\ hearts\ cards}{Total\ Number\ of\ cards}[/tex]
[tex]\rm{Probability(Diamond\ or\ club\ or\ hearts)=\dfrac{39}{52}=\dfrac{3}{4} = 0.75 = 75\%[/tex]
(c) Compute the probability of randomly selecting a three or club.
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.
[tex]\rm{Probability(three\ or\ club)=\dfrac{Number\ of\ three\ or\ club\ cards}{Total\ Number\ of\ cards}[/tex]
[tex]\rm{Probability(three\ or\ club)=\dfrac{16}{52}=0.3077 = 30.77\%[/tex]
Learn more about Probability:
https://brainly.com/question/743546
