2 cards of hearts and 4 cards of spades are missing from a pack of 52 cards. A card is drawn at random from the remaining pack. What is the probability of getting a black card?
- \(\frac {22}{52}\)
- \(\frac {22}{46}\)
- \(\frac {24}{52}\)
- \(\frac {24}{46}\)
The Correct Option is B
Solution and Explanation
Initially, a standard deck of cards has 52 cards.
There are 13 cards of each suit: hearts, diamonds, clubs, and spades.
Hearts and diamonds are red, while clubs and spades are black.
So there are 26 red cards and 26 black cards.
We are given that 2 cards of hearts are missing and 4 cards of spades are missing.
The total number of missing cards is $2 + 4 = 6$.
The number of cards remaining is $52 - 6 = 46$.
Originally, there were 13 spades, but 4 are missing.
So the number of spades remaining is $13 - 4 = 9$.
Originally, there were 13 clubs, and no clubs are missing.
So the number of clubs is 13. The total number of black cards remaining is $9 + 13 = 22$.
The probability of getting a black card from the remaining pack is the number of black cards remaining divided by the total number of cards remaining: $$ P(\text{black card}) = \frac{\text{Number of black cards remaining}}{\text{Total number of cards remaining}} = \frac{22}{46}$$
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