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Question
Assertion (A): Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is `1/3`.
Reason (R): Let E and F be two events with a random experiment, then `P(E/F) = (P(E ∩ F))/(P(E))`.
Options
Both (A) and (R) are true and (R) is the correct explanation of (A).
Both (A) and (R) are true, but (R) is not the correct explanation of (A).
(A) is true, but (R) is false.
(A) is false, but (R) is true.
Solution
Both (A) and (R) are true and (R) is the correct explanation of (A).
Explanation:
Two coins are tossed simultaneously.
Sample space i.e., possible outcomes are {HT, TH, HH, TT}
E = event of getting two heads
F = event of getting at least one head
P(E) = `1/4`, P(F) = `3/4`, P(E ∩ F) = `1/4`
`P(E/F) = (P(E ∩ F))/(P(F))`
= `((1/4))/((3/4))`
= `1/3`
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