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.

Answer 1

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`