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A deck of 52 cards contains cards numbered 1 through 13 in each of 4

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A deck of 52 cards contains cards numbered 1 through 13 in each of 4 [#permalink]

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New post 29 Jan 2018, 06:13
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A deck of 52 cards contains cards numbered 1 through 13 in each of 4 different colors. John will win $100 if he pulls a card numbered either 7 or 9 from the deck. What is the probability that John will win $100?

A. 1/52
B. 1/26
C. 1/13
D. 2/13
E. 4/13
[Reveal] Spoiler: OA

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Re: A deck of 52 cards contains cards numbered 1 through 13 in each of 4 [#permalink]

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New post 29 Jan 2018, 09:47
D

Sample set =52

Cards numbered 7 =4
Probability =4/52

Cards numbered 9 =4
Probability =4/52

Total Probability = 4/52 +4/52=8/52=2/13
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Re: A deck of 52 cards contains cards numbered 1 through 13 in each of 4 [#permalink]

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New post 29 Jan 2018, 11:14
Total probability= 8C1/52C1
=2/13
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Re: A deck of 52 cards contains cards numbered 1 through 13 in each of 4 [#permalink]

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New post 30 Jan 2018, 11:18
Bunuel wrote:
A deck of 52 cards contains cards numbered 1 through 13 in each of 4 different colors. John will win $100 if he pulls a card numbered either 7 or 9 from the deck. What is the probability that John will win $100?

A. 1/52
B. 1/26
C. 1/13
D. 2/13
E. 4/13


Since there are four 7’s and four 9’s, the probability that John wins $100 is 8/52 = 2/13.

Answer: D
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Re: A deck of 52 cards contains cards numbered 1 through 13 in each of 4 [#permalink]

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New post 31 Jan 2018, 01:34
Bunuel wrote:
A deck of 52 cards contains cards numbered 1 through 13 in each of 4 different colors. John will win $100 if he pulls a card numbered either 7 or 9 from the deck. What is the probability that John will win $100?

A. 1/52
B. 1/26
C. 1/13
D. 2/13
E. 4/13


Solution



    • Total cards = 52.
      o Number of cards that John pulls out = 1
      o Thus, total possible ways of pulling out any card = 52C1 =52 ways
    • To win $100, he needs to get either 7 or 9
      o There are cards of 4 colors and each color has cards numbered 1 to 13.
      o Thus, each color card with have 7 or 9 in it.
      o Total favorable cards available \(= 2 + 2 + 2 + 2 =8\) cards
      o And total ways to pull out one favorable card = 8C1 =8 ways
    • Therefore, the probability that John will win $100 \(= \frac{Favorable Cases}{Total Cases} = \frac{8}{52} = \frac{2}{13}\)

Correct Answer : Option D

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Re: A deck of 52 cards contains cards numbered 1 through 13 in each of 4   [#permalink] 31 Jan 2018, 01:34
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