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A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade is
- a)3/4
- b)52/867
- c)39/50
- d)22/425
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A pack of cards has one card missing. Two cards are drawn randomly and...
Let E1, E2, E3 and E4 be the events of losing a card of spades, clubs, hearts and diamonds, respectively.
Then, P(E1) = P(E2) = P(E3) = P(E4) = 13/52 = 1/4
Let E be the event of drawing 2 cards of spades from the remaining 51 cards.
Then, P(E/E1) = Probability of drawing 2 cards of spades, given that a card of spades is missing
P(E/E2) = Probability of drawing 2 cards of spades, given that a card of clubs is missing
Then, P(E1) = P(E2) = P(E3) = P(E4) = 13/52 = 1/4
Let E be the event of drawing 2 cards of spades from the remaining 51 cards.
Then, P(E/E1) = Probability of drawing 2 cards of spades, given that a card of spades is missing
P(E/E2) = Probability of drawing 2 cards of spades, given that a card of clubs is missing
P(E/E3) = Probability of drawing 2 spades, given that a card of hearts is missing
P(E/E4) = Probability of drawing 2 cards of spades, given that a card of diamonds is missing
∴ P(E1/E) = Probability of the lost card being a spade, given that 2 cards of spades are drawn from the remaining 51 cards
=
= 0.22
Hence, probability that the missing card is not a spade = 1 - 0.22 = 0.78
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Community Answer
A pack of cards has one card missing. Two cards are drawn randomly and...
To find the probability that the missing card is not a spade, we need to consider all the possible outcomes and the favorable outcomes.
Let's analyze the problem step by step:
1. Total number of cards in a pack: A standard pack of cards consists of 52 cards.
2. One card is missing: Since one card is missing, the total number of cards available is 51.
3. Two cards are drawn randomly: When two cards are drawn randomly, there are different possibilities for the types of cards that can be drawn. Let's consider each case separately:
a) Case 1: Both cards are spades
b) Case 2: One card is a spade and the other card is not a spade
c) Case 3: Both cards are not spades
4. Probability calculation:
a) Case 1: Both cards are spades
- The first card can be any one of the 13 spades.
- The second card can be any one of the remaining 12 spades.
- Therefore, the probability of drawing two spades is (13/51) * (12/50).
b) Case 2: One card is a spade and the other card is not a spade
- The first card can be any one of the 13 spades.
- The second card can be any one of the 39 non-spades.
- Therefore, the probability of drawing one spade and one non-spade is (13/51) * (39/50).
c) Case 3: Both cards are not spades
- The first card can be any one of the 39 non-spades.
- The second card can be any one of the remaining 38 non-spades.
- Therefore, the probability of drawing two non-spades is (39/51) * (38/50).
5. Summing up the probabilities:
- The probability of the missing card being a spade is the sum of the probabilities in cases 1 and 2.
- The probability of the missing card not being a spade is the probability in case 3.
- Therefore, the required probability is (13/51) * (12/50) + (13/51) * (39/50) = 39/50.
Hence, the correct answer is option 'C' (39/50).
Let's analyze the problem step by step:
1. Total number of cards in a pack: A standard pack of cards consists of 52 cards.
2. One card is missing: Since one card is missing, the total number of cards available is 51.
3. Two cards are drawn randomly: When two cards are drawn randomly, there are different possibilities for the types of cards that can be drawn. Let's consider each case separately:
a) Case 1: Both cards are spades
b) Case 2: One card is a spade and the other card is not a spade
c) Case 3: Both cards are not spades
4. Probability calculation:
a) Case 1: Both cards are spades
- The first card can be any one of the 13 spades.
- The second card can be any one of the remaining 12 spades.
- Therefore, the probability of drawing two spades is (13/51) * (12/50).
b) Case 2: One card is a spade and the other card is not a spade
- The first card can be any one of the 13 spades.
- The second card can be any one of the 39 non-spades.
- Therefore, the probability of drawing one spade and one non-spade is (13/51) * (39/50).
c) Case 3: Both cards are not spades
- The first card can be any one of the 39 non-spades.
- The second card can be any one of the remaining 38 non-spades.
- Therefore, the probability of drawing two non-spades is (39/51) * (38/50).
5. Summing up the probabilities:
- The probability of the missing card being a spade is the sum of the probabilities in cases 1 and 2.
- The probability of the missing card not being a spade is the probability in case 3.
- Therefore, the required probability is (13/51) * (12/50) + (13/51) * (39/50) = 39/50.
Hence, the correct answer is option 'C' (39/50).
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A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade isa)3/4b)52/867c)39/50d)22/425Correct answer is option 'C'. Can you explain this answer?
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