According to a study done in an office, 12 out of 30 employees were interested in doing work from home, if three employees were selected at random, what is the probability that at most two of them were interested in doing work from home?
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Answer:
192/203
Step-by-step explanation:
According to a study done in an office, 12 out of 30 employees were interested in doing work from home, if three employees were selected at random, what is the probability that at most two of them were interested in doing work from home?
Total 30 employee
randomly selected = 3
Total selection = ³⁰C₃ = 30 * 29 * 28/3 * 2 = 140 * 29 = 4060
at most two interest to work from home
= 0 or 1 or 2
¹⁸C₃ + ¹²C₁¹⁸C₂ + ¹²C₂¹⁸C₁
= 18 * 17 * 16/6 + 12 * 18 * 17/2 + (12 * 11 /2 )* 18
= 51 * 16 + 108 * 17 + 66 * 18
= 816 + 1836 + 1188
= 3840
Probability = 3840/4060
= 384/406
= 192/203
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