John and Dani go for an interview for two vacancies. The probability for the selection of John is 1/3 and whereas the probability for the selection of Dani is 1/5. What is the probability that only one of them is selected?
Select one:
a. 5/8
b. 3/5
c. 1/5
d. 2/5
Answers
Answer:
d. 2/5.
Step-by-step explanation:
Probability of one of them being selected, imply either John must be selected and Dani must not or Dani must be selected and John must not.
The probability of John's selection is 1/3, so that of his disselection is (1-1/3) = 2/3.
The probability of Dani's selection is 1/5, so that of his disselection is (1-1/5) = 4/5.
The probability of John's selection and Dani's disselection is 1/3 x 4/5 = 4/15.
The probability of Dani's selection and John's disselection is 2/3 x 1/5 = 2/15.
So the required probability is 4/15 + 2/15 = 6/15 = 2/5.
The answer is (d) 2/5
Given,
Probability of selection of John (A) = 1/3
Probability of selection of Dani (B) = 1/5
To Find,
Probability of selection of only one of them
Solution,
Probability of John not being selected (A)' = 1 - 1/3
= 2/3
Probability of Dani not being selected (B)' = 1 - 1/5
= 4/5
∴ The required probability = P(A) × P(B)' + P(A)' × P(B)
= 1/3 × 4/5 + 2/3 × 1/5
= 4/15 + 2/15
= 6/15
= 2/5
Hence, the required probability is 2/5.