Question:
From a pack of 52 cards, 3 cards are drawn at random. What is the probability that one is an ace, one is a queen, and one is a jack?
From a pack of 52 cards, 3 cards are drawn at random. What is the probability that one is an ace, one is a queen, and one is a jack?
Show Hint
Use combinations for drawing specific cards from a deck. Multiply individual selections and divide by total combinations.
Updated On: May 17, 2025
- \( \frac{19}{5525} \)
- \( \frac{21}{5525} \)
- \( \frac{17}{5525} \)
- \( \frac{16}{5525} \)
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Number of ways to choose:
- 1 ace from 4: \( ^4C_1 = 4 \)
- 1 queen from 4: \( ^4C_1 = 4 \)
- 1 jack from 4: \( ^4C_1 = 4 \)
Total favorable outcomes = \( 4 \cdot 4 \cdot 4 = 64 \)
Total ways to choose any 3 cards from 52:
\[
^{52}C_3 = \frac{52 \cdot 51 \cdot 50}{3 \cdot 2 \cdot 1} = 22100
\Rightarrow \text{Probability} = \frac{64}{22100} = \frac{16}{5525}
\]
Was this answer helpful?
0
0
Top Questions on Probability
- Two different dice are tossed together. Find the probability that the product of the number on the top of the dice is 6.
- Two dice are thrown. Defined are the following two events A and B: \[ A = \{(x, y) : x + y = 9\}, \quad B = \{(x, y) : x \neq 3\}, \] where \( (x, y) \) denote a point in the sample space. Check if events \( A \) and \( B \) are independent or mutually exclusive.
- In the following probability distribution, the value of p is:
- A die with numbers 1 to 6 is biased such that \( P(2) = \frac{3}{10} \) and the probability of other numbers is equal. Find the mean of the number of times number 2 appears on the die, if the die is thrown twice.
- The probability distribution of a random variable \( X \) is given by:
View More Questions
Questions Asked in AP EAPCET exam
- In \( \triangle ABC \), if \( r_1 = 4 \), \( r_2 = 8 \), \( r_3 = 24 \), then find \( a \)=
- AP EAPCET - 2024
- Triangles
The range of the real valued function \( f(x) =\) \(\sin^{-1} \left( \frac{1 + x^2}{2x} \right)\) \(+ \cos^{-1} \left( \frac{2x}{1 + x^2} \right)\) is:
- AP EAPCET - 2024
- Inverse Trigonometric Functions
The value of shunt resistance that allows only 10% of the main current through the galvanometer of resistance \( 99 \Omega \) is:
- AP EAPCET - 2024
- Current electricity
- If \( P(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e \) is a polynomial such that: \[ P(0) = 1, \quad P(1) = 2, \quad P(2) = 5, \] \[ P(3) = 10, \quad P(4) = 17, \] then find the value of \( P(5) \)=
- AP EAPCET - 2024
- Polynomials
- The area of the region enclosed by the curves \[ 3x^2 - y^2 - 2xy + 4x + 1 = 0 \] and \[ 3x^2 - y^2 - 2xy + 6x + 2y = 0 \] is:
- AP EAPCET - 2024
- Area under Simple Curves
View More Questions