MHT CET · Maths · Probability
A card is drawn at random from a well shuffled pack of 52 cards. The probability that it is black card or face card is
- A \(\frac{3}{13}\)
- B \(\frac{5}{13}\)
- C \(\frac{6}{13}\)
- D \(\frac{8}{13}\)
Answer & Solution
Correct Answer
(D) \(\frac{8}{13}\)
Step-by-step Solution
Detailed explanation
Here, \(\mathrm{n}(\mathrm{S})=52\)
Let event A : A black card is drawn. event \(B\) : A face card is drawn.
\(
n(A)=26, n(B)=12, n(A \cap B)=6
\)
Required probability
\(
\begin{aligned}
& =P(A \cup B) \\
& =P(A)+P(B)-P(A \cap B) \\
& =\frac{26}{52}+\frac{12}{52}-\frac{6}{52} \\
& =\frac{32}{52}=\frac{8}{13}
\end{aligned}
\)
Let event A : A black card is drawn. event \(B\) : A face card is drawn.
\(
n(A)=26, n(B)=12, n(A \cap B)=6
\)
Required probability
\(
\begin{aligned}
& =P(A \cup B) \\
& =P(A)+P(B)-P(A \cap B) \\
& =\frac{26}{52}+\frac{12}{52}-\frac{6}{52} \\
& =\frac{32}{52}=\frac{8}{13}
\end{aligned}
\)
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