Question 142
Two friends, Alka and Alkit appear for an interview for two vacancies for the same post in an Organisation. The probability of Alka's selection is 1/7 and Alkit is 1/ 5. What is the probability that only one of them will be selected?
Solution
Let
P(Alka selected) = 1/7 so P(Alka not selected) = 6/7
P(Alkit selected) = 1/5 sp P (Alkit not selected) = 4/5
So, the probability of only one being selected:
Case 1: Alka selected, Alkit not selected
$$\dfrac{1}{7}\times\dfrac{4}{5}=\dfrac{4}{35}$$
Case 2: Alka not selected, Alkit selected
$$\dfrac{6}{7}\times\dfrac{1}{5}=\dfrac{6}{35}$$
Total probability: $$\dfrac{4}{35}+\dfrac{6}{35}=\dfrac{10}{35}=\dfrac{2}{7}$$
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