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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
MCQ
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 $\frac{1}{3}$.
Reason $(R)$ : Let $E$ and $F$ be two events with a random experiment, then $P(F / E)=\frac{P(E \cap F)}{P(E)}$.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true, but Reason $(R)$ is not the correct explanation of the Assertion (A).
  • C
    Assertion (A) is true and Reason (R) is False.
  • D
    Assertion (A) is false but Reason (R) is true.
✓

Answer

Sample space $=\{ HH , HT , TH , TT \}$
Let $A$ be the event of coming up two heads
$\therefore \quad A=\{H H\} \Rightarrow P(A)=\frac{1}{4}$
and $B$ be the event of coming up atleast one head
$
\therefore \quad B=\{ HH , HT , TH \} \Rightarrow P(B)=\frac{3}{4}$
Also, $A \cap B=\{H H\} \Rightarrow P(A \cap B)=\frac{1}{4}$
So, required probability $=P(A / B)=\frac{P(A \cap B)}{P(B)}=\frac{\frac{1}{4}}{\frac{3}{4}}=\frac{1}{3}$
So, assertion is true.
Also, reason is true and it is the correct explanation of assertion.

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