Question

Please help!

Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that both cards are spades? Are these events independent?


A. 1/17: no, they are dependent events

B. 1/16: yes, they are independent events

C. 25/52: yes, they are independent events

D. 3/52: no, they are dependent events

Answer 1

Answer:
Choice A
1/17; no, they are dependent events

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Step-by-step explanation:

There are 13 spades and 52 cards total. So 13/52 = 1/4 is the probability of drawing one spade

If we do not replace the card we pull out, then the probability of another spade is 12/51 since there are 12 spades left out of 51 total.

Multiply the fractions 1/4 and 12/51 to get
(1/4)*(12/51) = (1*12)/(4*51) = 12/204 = 1/17

The two events are not independent because the second event (pulling out a second spade) depends entirely on what happens in the first event (pulling out a first spade). The fact that the probability is altered indicates we have dependent events.