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From a pack of 52 playing cards, three cards are drawn at random. Find the probability of drawing a king, a queen and jack.
- a)6/5525
- b)1/133
- c)1/143
- d)1/153
Correct answer is option 'A'. Can you explain this answer?
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Understanding the Problem
To find the probability of drawing a king, a queen, and a jack from a standard deck of 52 playing cards, we need to consider the total outcomes and the favorable outcomes.
Total Outcomes
- The total number of ways to choose any 3 cards from 52 is given by the combination formula:
\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
Here, \( n = 52 \) and \( r = 3 \).
- Thus,
\[ \binom{52}{3} = \frac{52 \times 51 \times 50}{3 \times 2 \times 1} = 22100 \]
Favorable Outcomes
- We need to find the number of ways to draw one king, one queen, and one jack.
- There are 4 kings, 4 queens, and 4 jacks in a deck. The number of ways to choose one of each is:
- Choose 1 king: 4 ways
- Choose 1 queen: 4 ways
- Choose 1 jack: 4 ways
- So, the total favorable outcomes are:
\[ 4 \times 4 \times 4 = 64 \]
Calculating Probability
- The probability \( P \) of drawing one king, one queen, and one jack is given by:
\[ P = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} \]
- Substituting the values:
\[ P = \frac{64}{22100} \]
- Simplifying this fraction:
\[ P = \frac{64}{22100} \approx \frac{6}{5525} \]
Thus, the probability of drawing a king, a queen, and a jack is \( \frac{6}{5525} \), matching option 'A'.
To find the probability of drawing a king, a queen, and a jack from a standard deck of 52 playing cards, we need to consider the total outcomes and the favorable outcomes.
Total Outcomes
- The total number of ways to choose any 3 cards from 52 is given by the combination formula:
\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
Here, \( n = 52 \) and \( r = 3 \).
- Thus,
\[ \binom{52}{3} = \frac{52 \times 51 \times 50}{3 \times 2 \times 1} = 22100 \]
Favorable Outcomes
- We need to find the number of ways to draw one king, one queen, and one jack.
- There are 4 kings, 4 queens, and 4 jacks in a deck. The number of ways to choose one of each is:
- Choose 1 king: 4 ways
- Choose 1 queen: 4 ways
- Choose 1 jack: 4 ways
- So, the total favorable outcomes are:
\[ 4 \times 4 \times 4 = 64 \]
Calculating Probability
- The probability \( P \) of drawing one king, one queen, and one jack is given by:
\[ P = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} \]
- Substituting the values:
\[ P = \frac{64}{22100} \]
- Simplifying this fraction:
\[ P = \frac{64}{22100} \approx \frac{6}{5525} \]
Thus, the probability of drawing a king, a queen, and a jack is \( \frac{6}{5525} \), matching option 'A'.
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From a pack of 52 playing cards, three cards are drawn at random. Find the probability of drawing a king, a queen and jack.a)6/5525b)1/133c)1/143d)1/153Correct answer is option 'A'. Can you explain this answer?
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