1. Draw 1 card from a standard deck of 52. Find the probability that it is a hea

Question

1. Draw 1 card from a standard deck of 52.

Find the probability that it is a heart or a king.

2. Draw 1 card from a standard deck of 52.

Find the probability that it is a club, given that it is a black card.

3. A bag contains 20 marbles: 5 red, 4 yellow, 8 blue, and 3 green.

Draw three marbles without replacement, one at a time. Find the probability that you get all red marbles.

4. A bag contains 20 marbles: 5 red, 4 yellow, 8 blue, and 3 green.

Draw three marbles without replacement, one at a time. Find the probability that you get at least one red.

5. Real estate ads suggest that 60% of homes for sale have garages, 20% have swimming pools, and 15% have both. What is the probability that a home for sale has a pool or a garage?

Explanation / Answer

1. There are 13 hearts and 3 other kings.

Probability = 16 / 52 = 0.3077.

2. Since the card is black it can be a spade or a club and there are equal number of cards of both.

Probability = 1/2 = 0.5.

3. Three red marbles can be chosen out of 5 in 5C3 ways.

There are 20 in all and 20C3 possibilities.

Probability = 5C3 / 20C3

= 10 / 1140

= 0.0088.

4. There are 4 yellow, 8 blue and 3 green marbles.

=> Probability that there is no red marble among the three

= 15C3 / 20C3

= 455 / 1140

= 0.3991

=> Probability that there is atleast one red marble

= 1 - 0.3991

= 0.6009.

5. P(A) = 60% = 0.6 P(B) = 20% = 0.2 P(A and B) = 15% = 0.15

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

= 0.6 + 0.2 - 0.15

= 0.65.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.