Question

Assertion :

From a well shuffled pack of $52$ playing cards a card is drawn at random. Two events $A$ and $B$ are defined as:
$A$: Red card is drawn; $B$: Card drawn is either a Diamond or Heart

Reason: $P\left(A\right)=\frac{1}{2}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Given,
Event $A$ is the probability of drawing red card from pack of $52$ cards.
$\therefore$ The probability $P\left(A\right)=\frac{26}{52}=\frac{1}{2}$ (since in a pack of $52$ cards there will be $26$ red cards)
Event $B$ is the probability of drawing diamond or heart card from pack of $52$ cards.
$\therefore$ The probability $P\left(A\right)=\frac{(13+13)}{52}=\frac{1}{2}$ (since in a pack of $52$ cards, there will be $13$ heart cards and $13$ diamond cards)