Test Index

VITEEE 2025 Paper

© examsnet.com

Question : 98 of 125

Marks: +1, -0

Two cards from an ordinary deck of 52 cards are missing. What is the probability that a random card drawn from this deck is a spade?

$\;\frac{3}{4}$
$\;\frac{2}{3}$
$\;\frac{1}{2}$
$\;\frac{1}{4}$

Solution:

Let

E

be the event that the randomly drawn card is a spade. Let

F_i

be the event that

i

spades nre missing from the 52-card, for

i

can take values

0,1,2

\;P(E)=P\left(\frac{E}{F_0}\right)P(F_0)+P\left(\frac{E}{F_1}\right)P(F_1)+P\left(\frac{E}{F_2}\right)P(F_2)

\;=\;\frac{13}{50}\;\frac{\binom{13}{0}\binom{39}{2}}{\binom{52}{2}}+\;\frac{12}{50}\;\frac{\binom{13}{1}\binom{39}{1}}{\binom{52}{2}}+\;\frac{11}{50}\;\frac{\binom{13}{2}\binom{39}{0}}{\binom{52}{2}}=\;\frac{1}{4}

© examsnet.com

Go to Question:

Prev Question

Next Question