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There are 5 red caps and 4 black caps in a sale. They have got all mix

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There are 5 red caps and 4 black caps in a sale. They have got all mix [#permalink] New post   26 Jul 2020, 20:05
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There are 5 red caps and 4 black caps in a sale. They have got all mixed up with each other. What is the probability of getting a matched cap if two caps are drawn at random?
(a) 7/9
(b) 4/9
(c) 2/9
(d) 5/9
(e) 2/3
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B
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Re: There are 5 red caps and 4 black caps in a sale. They have got all mix [#permalink] New post   26 Jul 2020, 20:45
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Probability = Favorable Outcomes by Total Outcomes

Favorable Outcomes = Choosing 2 caps of the same color i.e either 2 red or 2 black = 5C2 + 4C2 = 10 + 6 = 16

Total Outcomes = Choosing any 2 caps out of the 7 available = 9C2 = 36

The required probability = 16 / 36 = 4 / 9

Option B

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Re: There are 5 red caps and 4 black caps in a sale. They have got all mix [#permalink] New post   26 Jul 2020, 22:10
There are 5 red caps and 4 black caps in a sale. They have got all mixed up with each other. What is the probability of getting a matched cap if two caps are drawn at random?
(a) 7/9
(b) 4/9
(c) 2/9
(d) 5/9
(e) 2/3

- Total caps = 5+4 = 9
To get the same color cap twice, either both must be red or both must be blue.
For red: \(\frac{5}{9} * \frac{4}{8}\)
+
For black: \(\frac{4}{9} * \frac{3}{8}\)
= 4/9

Answer B
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Re: There are 5 red caps and 4 black caps in a sale. They have got all mix [#permalink] New post   26 Jul 2020, 22:56
Alternatively,
=> Probability of Getting two same coloured caps = 1 - probability of getting different colored caps

=> Ps = 1 - Pd
=> Ps = 1 - (5C1*4C1)/9C2
=> Ps = 1 - 5*4/{(9*8)/2}
=> Ps = 1 - 5*4/9*4
=> Ps = 1 - 5/9
=> Ps = 4/9

Answer is B

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Re: There are 5 red caps and 4 black caps in a sale. They have got all mix [#permalink]
26 Jul 2020, 22:56
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