A card is randomnly selected from a deck of 52 cards and a die is rolled. Find the probability of obtaining?

Question

a club and an even number on the die

a club or and even number on the die

Answer 1

Event A: chance of a club is 13/52 or 1/4
Event B: chance of an even number is 3/6 or 1/2

The probability of A and B is:
P(A) * P(B)
= 1/4 x 1/2
= 1/8

The probability of A *or* B is:
P(A) + P(B) - P(A)*P(B) = 1/4 + 1/2 - 1/8
= 3/4 - 1/8
= 6/8 - 1/8
= 5/8

Answer 2

For any two events, A and B:

P(A or B) = P(A) + P(B) - P(A and B)

in symbols this is:

P(A U B) = P(A) + P(B) - P(A ∩ B)

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if A and B are independent events then
P(A ∩ B) = P(A) * P(B)

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In your question let A be the event of drawing a club
Let B be the event of rolling an even number on the die. Assuming that the die is fair then:

P(A) = 1/4
P(B) = 1/2

P(A ∩ B) = 1/4 * 1/2 = 1/8 because A and B are independent.

P(A U B) = 1/4 + 1/2 - 1/8 = 5/8

Answer 3

Club and even number = 13/52 X 3/6

Club or even number = 13/52 + 3/6 - (13/52 X 3/6)

Answer 4

club in the cards

13/52 = 1/4

even number on die
3/6 = 1/2

Answer 5

1/8

Answer 6

P(A) is prob. of club = 1/4
P(B) is prob. of even number = 1/2

P (A and B)
1/8


P (A or B)
1/4 + 1/2 - 1/8
5/8