Respuesta :
To find the answer:
The probability of getting a ten:
=4/52
The probability of getting a king:
=4/52
The probability of getting a diamond:
=52×1/4
=13/52
However,there would be king and ten of diamond which overlapped and therefore -2/52 would be in the equation.
We can then sum up to find the equation:
=4/52+4/52+13/52-2/52
=21/52-2/52
=19/52
Therefore the answer is 19/52.
Hope it helps!
The probability of getting a ten:
=4/52
The probability of getting a king:
=4/52
The probability of getting a diamond:
=52×1/4
=13/52
However,there would be king and ten of diamond which overlapped and therefore -2/52 would be in the equation.
We can then sum up to find the equation:
=4/52+4/52+13/52-2/52
=21/52-2/52
=19/52
Therefore the answer is 19/52.
Hope it helps!
The probability of getting a ten, a king, or a diamond from a deck is 19/52. This is obtained by using the probability definition.
What is probability?
- The probability is the measure of an event occurring.
- Probability is given by the ratio of the number of outcomes to the total number of possible outcomes.
- The representation is P(A) = [tex]\frac{n(A)}{n(S)}[/tex] where A is the event, n(A) -the number of equally likely events, and n(S) -the total number of outcomes of the sample
- The probability of two or more events is represented as P(A∪B∪C) = P(A) + P(B) +P(C) - P(A∩B) - P(B∩C) - P(C∩A) + P(A∩B∩C)
Calculating the probability for the given events:
Given that,
One card is drawn from the deck of cards (52 cards in the deck)
The probability of getting a ten from the deck is
P(T) = 4/52 (since there are 4 tens in the whole 52 cards)
The probability of getting a king from the deck is
P(K) = 4/52 (since there are 4 kings in the 52 cards)
The probability of getting a diamond from the deck is
P(D) = 13/52 (since there are 13 diamond cards in the deck)
The probability of getting a ten and a king from the deck is not possible. So, P(T∩K) = 0
The probability of getting a king and a diamond from the deck is
P(K∩D) = 1/52 (since there is 1 king in 13 diamonds)
The probability of getting a diamond and a ten from the deck is
P(D∩T) = 1/52 (since there is 1 ten in the 13 diamonds)
The probability of getting a ten and a king and a diamond from the deck is
P(T∩K∩D) = 0 (since it is not possible that the card should be ten, king, and a diamond)
So, the probability of getting a ten, a king, or a diamond is
P(T∪K∪D) = P(T) + P(K) + P(D) - P(T∩K) - P(K∩D) - P(D∩T) + P(T∩K∩D)
On substituting,
P(T∪K∪D) = 4/52 + 4/52 + 13/52 - 0 - 1/52 - 1/52 + 0
= 19/52
Thus, the probability of getting a ten, a king, or a diamond is 19/52.
Learn more about probabilities here:
https://brainly.com/question/5858025
#SPJ2
