You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck.(a) Are the outcomes on the two cards independent? Why?Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.No. The events cannot occur together.     Yes. The events can occur together.No. The probability of drawing a specific second card depends on the identity of the first card.(b) Find P(ace on 1st card and king on 2nd). (Enter your answer as a fraction.)(c) Find P(king on 1st card and ace on 2nd). (Enter your answer as a fraction.)(d) Find the probability of drawing an ace and a king in either order. (Enter your answer as a fraction.)

Question
Asked Sep 19, 2019

You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck.

(a) Are the outcomes on the two cards independent? Why?
Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.No. The events cannot occur together.     Yes. The events can occur together.No. The probability of drawing a specific second card depends on the identity of the first card.

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


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


(d) Find the probability of drawing an ace and a king in either order. (Enter your answer as a fraction.)
check_circleExpert Solution
Step 1

(a)

If the outcomes of the two cards are independent, then the probability of drawing a specific second card is the same regardless of the identity of the first drawn card.

Hence, the probability of drawing a specific second card is the same regardless of the identity of the first drawn card.

Thus, the correct statement is “Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card”.

(b)

The value of P (ace on 1st card and king on 2nd) is obtained below:

4
4
P(ace on lst card and king on 2nd)
X
52 52
1 1
13 13
1
169
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Image Transcriptionclose

4 4 P(ace on lst card and king on 2nd) X 52 52 1 1 13 13 1 169

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Step 2

Thus, the value of P (ace on 1st card and king on 2nd) is 1/169.

(c)

The value of P(king on 1st card and ace on 2nd) is obtained below:

P(king on lst card and ace on 2nd)
52 52
1 1
13 13
1
169
help_outline

Image Transcriptionclose

P(king on lst card and ace on 2nd) 52 52 1 1 13 13 1 169

fullscreen
Step 3

Thus, the value of P(king on 1st card and ace on 2nd) is 1/169.

(d)

The probability of drawing an...

P(ace on 1st card and king on 2nd)
+P(king on 1st card and ace on 2nd)
1 1
+
169
169
2
169
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P(ace on 1st card and king on 2nd) +P(king on 1st card and ace on 2nd) 1 1 + 169 169 2 169

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