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Two cards are drawn successively and without replacement from an ordinary deck of playing cards Compute the probability of drawing

a. Two hearts.

b. A heart on the first draw and a club on the second draw.

c. A heart on the first draw and an ace on the second draw.

 

Hint: In part (c), note that a heart can be drawn by getting the ace of hearts or one of the other 12 hearts.

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Karol A.
Karol A.Lv10
4 Apr 2021
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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

24. You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. Express your answer as a simplified fraction.

25. You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a King and the second card is a queen. Express your answer as a simplified fraction.

ou draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second.

(a) Are the outcomes on the two cards independent? Why?

No. The probability of drawing a specific second card depends on the identity of the first card.

No. The events cannot occur together.

Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.

Yes. The events can occur together.

(b) Find P(3 on 1st card and 10 on 2nd). (Enter your answer as a fraction.)

(c) Find P(10 on 1st card and 3 on 2nd). (Enter your answer as a fraction.)

(d) Find the probability of drawing a 10 and a 3 in either order. (Enter your answer as a fraction.)

9. Identify why this assignment of probabilities can not be legitimate.

 

a. P(A & B) can not be greater than either P(A) or P(B).

b. A and B are not given as mutually exclusive events.

c. P(A|B) is not known.

d. A and B are not given as independent events.

e. none of these.

 

10. Suppose a box contains 3 detective light bulbs and 12 good bulbs. Two bulbs are chosen from the box without replacement. Find the probability that one of the bulbs drawn is good and one is defective.

A. 12/35

B. 6/35

C. 3/14

D. 3/70

E. None of these

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