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Sagot :
The required probabilities are:
A) P(D or 5) = 4/13
B) P(H and J) = 1/13
C) P(J or 8) = 2/13
D) P(H or S) = 1/2
E) P(R and F) = 3/26
F) P(R or Q) = 7/13
What is probability?
The ratio of favorable outcomes to the total outcomes of an event is said to be its probability.
P(E) = n(E)/n(S)
Calculation:
It is given that a single card is drawn at random from a standard deck of 52 cards.
So, the sample space consists of 52 cards in total
From those,
4 suits: Hearts, Clubs, Spades, Diamonds
Each of the suit has 13 cards: { Ace, 2,3,4,5,6,7,8,9,10, Jack, Queen, King}
There are 26 Red cards and 26 Black cards.
A) The probability of drawing a diamond or a 5:
P(D or 5) = P(D) + P(5) - P(D and 5)
= 13/52 + 4/52 - 1/52
= 16/52 = 4/13
B) The probability of drawing a heart and a jack:
P(H and J) = P(H) × P(J) (Since they are independent events)
= 13/52 × 4/13
= 1/13
C) The probability of drawing a jack or 8:
P(J or 8) = P(J) + P(8) - P(J and 8)
= 4/52 + 4/52 - 0
= 2/13
D) The probability of drawing a heart or a spade:
P(H or S) = P(H) + P(S) - P(H and S)
= 13/52 + 13/52 - 0
= 26/52 = 1/2
E) The probability of drawing a red and face card:
P(R and F) = P(R) × P(F) (Since they are independent)
= 26/52 × 12/52
= 1/2 × 3/13
= 3/26
(There are three face cards- jack, king, and queen: each of 4)
F) The probability of drawing a red card or a queen:
P(R or Q) = P(R) + P(Q) -P(R and Q)
= 26/52 + 4/52 - 2/52
= 28/52 = 7/13
Thus, the required probabilities are calculated.
Learn more about the probability here:
https://brainly.com/question/13604758
#SPJ1
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