Q46 / 100 · BITSAT 2023 (Memory Based Paper 1) · Mathematics
The probability that a card drawn from a pack of 52 cards will be a diamond or king is:
- A$\frac{1}{52}$
- B$\frac{2}{13}$
- Correct answerC$\frac{4}{13}$
- D$\frac{1}{13}$
Solution
Total no. of cards $=52$
13 cards are diamonds and 4 cards are king.
There is only one card which is a king of diamond.
$\therefore \mathrm{P}($ card is diamond $)=\frac{13}{52}, \mathrm{P}$ (card is king)
$=\frac{4}{52}$
$\mathrm{P}($ card is king of diamond $)=\frac{1}{52}$
$\therefore \quad P$ (card is diamond or king)
$=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{16}{52}=\frac{4}{13}$
13 cards are diamonds and 4 cards are king.
There is only one card which is a king of diamond.
$\therefore \mathrm{P}($ card is diamond $)=\frac{13}{52}, \mathrm{P}$ (card is king)
$=\frac{4}{52}$
$\mathrm{P}($ card is king of diamond $)=\frac{1}{52}$
$\therefore \quad P$ (card is diamond or king)
$=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{16}{52}=\frac{4}{13}$
Hence, the correct answer is option: 'C'.