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18 May 2018, 00:50
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
80% (01:28) correct
20%
(01:38)
wrong
based on 122
sessions
History
Date
Time
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Not Attempted Yet
A drawer contains 6 brown socks and 4 black socks. What is the probability that the first two socks pulled from the drawer will be of the same color?
A. \(\frac{1}{3}\)
B. \(\frac{7}{15}\)
C. \(\frac{1}{2}\)
D. \(\frac{8}{15}\)
E. \(\frac{2}{3}\)
A. \(\frac{1}{3}\)
B. \(\frac{7}{15}\)
C. \(\frac{1}{2}\)
D. \(\frac{8}{15}\)
E. \(\frac{2}{3}\)
18 May 2018, 02:49
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Solution
Given:
• A drawer contains 6 brown socks and 4 black socks
To find:
• The probability that the first two socks pulled from the drawer will be of the same color
Approach and Working:
• The probability that first two socks pulled will be of same color =
Probability that both the socks are brown (or) Probability that both the socks are black
= \(\frac{6}{10} * \frac{5}{9} + \frac{4}{10} * \frac{3}{9} = \frac{30}{90} + \frac{12}{90} = \frac{42}{90} = \frac{7}{15}\)
Hence, the correct answer is option B.
Answer: B
18 May 2018, 06:20
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Bunuel
Required probability = number of ways of selecting 2 socks belonging to same colour / number of ways of selecting 2 socks.
Total number of socks = 10.
Number of ways of selecting 2 socks from 10 socks = 10C2 = (10*9)/2 = 45
Number of ways of selecting 2 socks that belong to the same colour = number ways of selecting 2 brown socks from 6 + number of ways of selecting 2 black socks from 4
= 6C2 + 4C2 = (6*5)/2 + (4*3)/2 = 15 + 6 = 21
Required probability = 21/45 = 7/15
