Question

Problem 6: Dice and cards

An experiment consists of rolling a single die and selecting a card from a standard deck. Use this information to answer the following three questions:

1

What is the probability of rolling an even number and selecting the ace of hearts?

2

What is the probability of rolling a 3 and selecting a diamond?

3

What is the probability of selecting an even number and selecting a king?

Answer 1

1.

Now since selecting an even number and selecting a card from a deck are independent events therefore:-

P(Rolling an even number and selecting the ace of hearts)

= P(Rolling an even number) * P(selecting the ace of hearts)

= 1/2 * 1/52

= 1/104

2.

P(Rolling a 3 and selecting a diamond)

= P(Rolling a 3) * P(selecting a diamond)

= 1/6 * 13/52

= 1/24

3.

P(selecting an even number and selecting a king)

=P(selecting an even number) * P(selecting a king)

= 1/2 * 4/52

= 1/26

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