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08 Jul 2020, 09:00
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A
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Difficulty:
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A Chartered Accountant applies for a job in two firms X & Y. The probability of his being selected in firm X is 0.7, and being rejected at Y is 0.5 and the probability of rejection at least one of his applications is 0.6. What is the probability that he will be selected in one of the firms?
A) 0.8
B) 0.2
C) 0.4
D) 0.7
E) 0.5
Posted from my mobile device
A) 0.8
B) 0.2
C) 0.4
D) 0.7
E) 0.5
Posted from my mobile device
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08 Jul 2020, 09:29
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Note:
P(A)= probability that he gets selected in firm A; P(~A)= probability that he gets rejected at firm A.
All other symbols have the usual meaning.
Solution:
P(X)= 0.7 => P(~X)= 0.3
P(~Y)= 0.5 => P(Y)= 0.5
Now, it is given that P(~X U ~Y)= 0.6
=> P(~X)+P(~Y)-P(~X ⋂ ~Y)= 0.6
=> 0.3+0.5- P(~X ⋂ ~Y) =0.6
=> P(~X ⋂ ~Y)= 0.2
This means the probability that the person is rejected by both the firms is 0.2.
Hence, the probability that the person would be selected by at least one of the firm is 0.8
P(A)= probability that he gets selected in firm A; P(~A)= probability that he gets rejected at firm A.
All other symbols have the usual meaning.
Solution:
P(X)= 0.7 => P(~X)= 0.3
P(~Y)= 0.5 => P(Y)= 0.5
Now, it is given that P(~X U ~Y)= 0.6
=> P(~X)+P(~Y)-P(~X ⋂ ~Y)= 0.6
=> 0.3+0.5- P(~X ⋂ ~Y) =0.6
=> P(~X ⋂ ~Y)= 0.2
This means the probability that the person is rejected by both the firms is 0.2.
Hence, the probability that the person would be selected by at least one of the firm is 0.8
08 Jul 2020, 11:42
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Explanation:
Let event X – he will be selected in firm X
Event Y – he will be selected in firm Y.
Then we have: ?(?) = 0.7, ?(?̅) = 0.3, ?(?̅) = ?(?) = 0.5, ?(?̅ ∪ ?̅) = 0.6.
Using the following equalities:
?(?̅ ∪ ?̅) = ?(?̅) + ?(?̅) − ?(?̅ ∩ ?̅),
0.6 = 0.3 + 0.5 − ?(?̅ ∩ ?̅),
?(?̅ ∩ ?̅) = 0.2.
?(? ∪ ?) = 1 − ?(?̅∪̅?̅) = 1 − ?(?̅ ∩ ?̅).
?(? ∪ ?) = 1 − 0.2 = 0.8
IMO-A
Let event X – he will be selected in firm X
Event Y – he will be selected in firm Y.
Then we have: ?(?) = 0.7, ?(?̅) = 0.3, ?(?̅) = ?(?) = 0.5, ?(?̅ ∪ ?̅) = 0.6.
Using the following equalities:
?(?̅ ∪ ?̅) = ?(?̅) + ?(?̅) − ?(?̅ ∩ ?̅),
0.6 = 0.3 + 0.5 − ?(?̅ ∩ ?̅),
?(?̅ ∩ ?̅) = 0.2.
?(? ∪ ?) = 1 − ?(?̅∪̅?̅) = 1 − ?(?̅ ∩ ?̅).
?(? ∪ ?) = 1 − 0.2 = 0.8
IMO-A
