If a card is selected at random from a deck of 52 cards, then the probability of getting a red face card is
- \(\frac{3}{26}\)
- \(\frac{3}{13}\)
- \(\frac{2}{13}\)
- \(\frac{1}{2}\)
The Correct Option is A
Solution and Explanation
A deck of 52 cards has 26 red cards (13 diamonds and 13 hearts). Each suit has 3 face cards (Jack, Queen, and King). Hence, the total number of red face cards is: \[ 3 (\text{face cards in hearts}) + 3 (\text{face cards in diamonds}) = 6 \] Thus, the probability of selecting a red face card is: \[ \text{Probability} = \dfrac{\text{Number of red face cards}}{\text{Total number of cards}} = \dfrac{6}{52} = \dfrac{3}{26} \]
The correct option is (A): \(\frac{3}{26}\)
Top Questions on Probability
Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy, 200 maintained average health and 100 had a poor health record.
Let \( A_1 \): People with good health,
\( A_2 \): People with average health,
and \( A_3 \): People with poor health.
During a pandemic, the data expressed that the chances of people contracting the disease from category \( A_1, A_2 \) and \( A_3 \) are 25%, 35% and 50%, respectively.
Based upon the above information, answer the following questions:
(i) A person was tested randomly. What is the probability that he/she has contracted the disease?}
(ii) Given that the person has not contracted the disease, what is the probability that the person is from category \( A_2 \)?- If A and B are two events such that $P(B) = \frac{1}{5}$, $P(A | B) = \frac{2}{3}$ and $P(A \cup B) = \frac{3}{5}$, then $P(A)$ is :
- If \( P(A) = \frac{1}{5}, P(B) = \frac{3}{5} \) and \( P(A \cap B) = \frac{2}{5} \), then \( P(A' \cup B') \) is :
- Bag I contains 4 white and 5 black balls. Bag II contains 6 white and 7 black balls. A ball drawn randomly from Bag I is transferred to Bag II and then a ball is drawn randomly from Bag II. Find the probability that the ball drawn is white.
- A meeting will be held only if all three members A, B and C are present. The probability that member A does not turn up is 0.10, member B does not turn up is 0.20 and member C does not turn up is 0.05. The probability of the meeting being cancelled is:
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