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29 May 2016, 03:44
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In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability that the worker is under 25 years old?
(A) 0.30
(B) 0.25
(C) 0.45
(D) 0.70
(E) 0.90
(A) 0.30
(B) 0.25
(C) 0.45
(D) 0.70
(E) 0.90
29 May 2016, 04:22
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Percentage of male worker = 48
Percentage of female worker = 52
Let total number of workers = 1000
number of male workers= 480
number of female workers = 520
Number of male age 25 or older = (4/10)*480 = 192
Number of female age 25 or older =(2/10)*520 = 104
Total number of workers 25 or older = 192+104 = 296
Total number of workers under 25 = 1000 - 296 = 704
Probability that a worker randomly selected is under 25 years old = 704/1000 = .704
Alternatively , since the answer options are not close , we can use estimation here .
Percentage of male worker 25 or older = (4/10)*48 = 20 % approx
Percentage of female worker 25 or older = (2/10)*52 = 10 % approx
Percentage of total worker 25 or older = 30 %
Percentage of total worker under 25 = 70 %
Probability that a worker randomly selected is under 25 years old = .7
Answer D
Percentage of female worker = 52
Let total number of workers = 1000
number of male workers= 480
number of female workers = 520
Number of male age 25 or older = (4/10)*480 = 192
Number of female age 25 or older =(2/10)*520 = 104
Total number of workers 25 or older = 192+104 = 296
Total number of workers under 25 = 1000 - 296 = 704
Probability that a worker randomly selected is under 25 years old = 704/1000 = .704
Alternatively , since the answer options are not close , we can use estimation here .
Percentage of male worker 25 or older = (4/10)*48 = 20 % approx
Percentage of female worker 25 or older = (2/10)*52 = 10 % approx
Percentage of total worker 25 or older = 30 %
Percentage of total worker under 25 = 70 %
Probability that a worker randomly selected is under 25 years old = .7
Answer D
29 May 2016, 04:43
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Bunuel
Hi,
a quick method would be to take advantage of the spread of choices..
we can see the % of M and F are almost SAME 52:48.... lets take them same...
Next is how many are LESS than 25 years-
60% of M and 80% of F fall in this category...
Since the number of M and F are same, our answer will be closer to the average of the % of M and F BELOW 25..
so \(\frac{60+80}{2} = 70\)
Prob = \(\frac{70}{100} = 0.7\)
D
