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प्रश्न
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))`.
विकल्प
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.
उत्तर
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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