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?

Question

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? (A) (3/4) (B) (2/3) (C) (1/2) (D) (1/4)

Tardigrade Admin · Accepted Answer

Let E be the event that the randomly drawn card is a spade. Let Fi be the event that spades are missing from the 50-card (defective) deck, for i = 0, 1, 2. We want P(E), which we compute by conditioning on how many spades are missing from the original deck: P(E) = P(E|F0) P(F0) + P(E|F1) P(F1) + P(E|E2) P(F2) = (13/50) ( binom130 binom392/ binom522)+(12/50) ( binom131 binom391/ binom522)+(11/50) ( binom132 binom390/ binom522) = (1/4)

Q. 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?

$\frac{3}{4}$

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{4}$

Q. 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?

43​

32​

21​

41​

Q. 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?

$\frac{3}{4}$

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{4}$