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Probability

Short Answer Type

861.

Fatima and John appear in an interview for two vacancies in the same post. The probability of Fatima's selection is $1 over 7 space and space$ that of John's selection is $1 fifth.$ What is the probability that none of them will be selected.

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862. Arun and Tarun appear for an interview for two vacancies. The probability of Arun's selection is $1 third$ and that of Tarun's selection is $1 fifth.$ Find the probability that only one of them will be selected.

Let A denote the event ‘Arun is selected’ and B denote the event ‘Tarun is selected’

therefore space space space straight P left parenthesis straight A right parenthesis space equals space 1 third comma space space straight P left parenthesis straight B right parenthesis space equals space 1 fifth

Also A and B are independent. A and not B are independent, not A and B are independent.
P (only one of them is selected)
= P ('A and not B' or 'B and not A')
= P(A and not B) + P(B and not A)
= P(A) P(not B) + P(B) P(not A)

space equals space straight P left parenthesis straight A right parenthesis space open square brackets 1 minus straight P left parenthesis straight B right parenthesis close square brackets space plus space straight P left parenthesis straight B right parenthesis space open square brackets 1 minus straight P left parenthesis straight A right parenthesis close square brackets

equals space 1 third cross times open square brackets 1 minus 1 fifth close square brackets plus 1 fifth open square brackets 1 minus 1 third close square brackets space equals space 1 third cross times 4 over 5 plus 1 fifth cross times 2 over 3 equals space 4 over 15 plus 2 over 15 equals space 6 over 15 equals space 2 over 5.

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863. Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal’s selection is

1 third

and that of Monica’s selection is

4 over 5.

Find the probability that only one of them will be selected.

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864. Surjit and Sachdev appeared for an interview. The probability of their selection is

1 third space and space 1 over 6

respectively. Find the probability both selected.

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865. Surjit and Sachdev appeared for an interview. The probability of their selection is

1 third space and space 1 over 6

respectively. Find the probability only one of them selected.

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866. Surjit and Sachdev appeared for an interview. The probability of their selection is

1 third space and space 1 over 6

respectively. Find the probability neither of them selected.

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867. Balwant and Kulwant appeared for an interview. The probability of their selection is

1 third space and space 1 fifth

respectively. Find the probability both selected.

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868. Balwant and Kulwant appeared for an interview. The probability of their selection is

1 third space and space 1 fifth

respectively. Find the probability only of them selected.

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869. Balwant and Kulwant appeared for an interview. The probability of their selection is

1 third space and space 1 fifth

respectively. Find the probability neither of them selected.

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Long Answer Type

870. Navdeepika and Meenakshi appeared for an interview. The probability of their selection is

1 third space and space 1 fourth

respectively. Find the probability of
(i) both selected.
(ii) only one of them selected
(iii) neither of them selected.

78 Views