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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.

80 Views

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.

135 Views

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.

91 Views

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.

93 Views

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.

89 Views

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.

90 Views

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.

101 Views

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.

95 Views

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.

92 Views

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.

Let A : Navdeepika is selected
B : Meenakshi is selected
$therefore space space space space space space straight P left parenthesis straight A right parenthesis space equals 1 third comma space space space straight P left parenthesis straight B right parenthesis space equals 1 fourth$
Clearly A and B are independent.
(i) P(both selected) = $straight P left parenthesis straight A space intersection space straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis space straight P left parenthesis straight B right parenthesis$
$equals space 1 third cross times 1 fourth space equals space 1 over 12$
(ii) P(only one 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)
= P(A) [1 - P(B)] + P(B) [1 - P(A)]
$equals space 1 third open parentheses 1 minus 1 fourth close parentheses space plus space 1 fourth space open parentheses 1 minus 1 third close parentheses equals space 1 third cross times 3 over 4 plus 1 fourth cross times 2 over 3 space equals space 3 over 12 plus 2 over 12 space equals 5 over 12$
(iii) P(neither selected) = P(not A and not B) = P(not A) P(not B)
$equals space left square bracket space 1 space minus space straight P left parenthesis straight A right parenthesis right square bracket space space space left square bracket 1 space minus space straight P left parenthesis straight B right parenthesis right square bracket equals space open parentheses 1 minus 1 third close parentheses space open parentheses 1 minus 1 fourth close parentheses space equals 2 over 3 cross times 3 over 4 space equals 1 half$