Question

When selecting a card from an ordinary deck of cards, what is the probability of getting a King?

When selecting a card from an ordinary deck of cards, what is the probability of getting a black card or a red card?

When selecting a card from an ordinary deck of cards, what is the probability of getting a 7 AND a heart?

When selecting a card from an ordinary deck of cards, what is the probability of getting a 7 OR a heart?

The probability of rolling a die and getting a number greater than 8 is:

What is the number of outcomes in the sample space if two dice are rolled?

When selecting a card from an ordinary deck of cards, what is the probability of getting a diamond or a spade?

Answer 1

1) Total no of cards in the deck = n(S) = 52

No of kings in the deck, N(E) = 4

So, the probability of getting a King = P(E) = 4/52 = 1/13

2) Total no of cards in the deck = n(S) = 52

No of black or red cards in the deck, N(E) = 52

(since the deck has either red or black card)

So, the prob. of getting a black or a red card = 52/52 = 1

3) Total no of cards in the deck = n(S) = 52

No of cards which is both a heart & 7, N(E) = 1

So, the probability of getting a 7 AND a heart = 1/52

4) Total no of cards in the deck = n(S) = 52

n( Cards with no 7) = 4, n(Hearts) = 13, n(Heart & 7) = 1

So, n(Hearts or a 7) = 4+13-1 = 16

So, the probability of getting a 7 OR a heart = 16/52 = 4/13

5) The probability of rolling a die and getting a number greater than 8 = 0

Because in a die maximum result we can get is 6

6) For one dice, no of outcomes = 6

So when two dice are rolled simultaneously, no of outcomes = 6•6 = 36

7) Total no of cards in the deck = n(S) = 52

No of diamond or spade in the deck, N(E) = 26

So, P(diamond or spade) = 26/52 = 1/2