Q. 305.0( 1 Vote )

# Fatima and John appear in an interview for two vacancies for the same post. The probability of Fatima’s selection is 1/7 and that of John’s selection is 1/5. What is the probability that

i. Both of them are selected

ii. Only one of them will be selected

iii. None of them will be selected

Answer :

Given that,

⇒ P(F_{S}) = P(Fatima’s selection)

⇒

⇒ P(F_{N}) = P(Not selecting Fatima)

⇒

⇒

⇒ P(J_{S}) = P(John’s selection)

⇒

⇒ P(J_{N}) = P(Not selecting John)

⇒

⇒

We need to find:

i. Both of them will be selected

ii. Only one of them will be selected

iii. None of them will be selected

⇒ P(S_{both}) = P(Both of them are selected)

Since selection of each person is an independent event their probabilities multiply each other

⇒

⇒

⇒

⇒ P(S_{one}) = P(Only one of them is selected)

⇒ P(S_{one}) = P(only Fatima is selected) + P(only John is selected)

Since selection of each person is an independent event their probabilities multiply each other

⇒

⇒

⇒

⇒ P(S_{none}) = P(None of them are selected)

Since selection of each person is an independent event their probabilities multiply each other

⇒

⇒

⇒

∴ The required probabilities are .

Rate this question :

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

Mathematics - Board PapersA speaks truth in 75% and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?

RD Sharma - Volume 2Two cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Find the probability of exactly one ace.

RD Sharma - Volume 2