All Exams Test series for 1 year @ ₹349 only
Question

A committee has 6 men and 4 women. One member is selected randomly which is woman only. What is the probability that she belongs to a subgroup of 2 senior women?

This question was previously asked in
NDA 2 2026 GAT Question Paper (13-Sep-2026)
The correct answer is

1/2

Given that the selected member is a woman, the sample space reduces to the 4 women in the committee. Since 2 of these 4 women form the senior subgroup, the required conditional probability is \(\frac{2}{4}=\frac{1}{2}\).

Was this answer helpful?

Similar Questions

  1. A and B are two events such that A̅ and B̅ are mutually exclusive. If P(A) = 0.5 and P(B) = 0.6, then what is the value of P(A|B)?

  2. For two dependent events A and B, it is given that P(A) = 0.2 and P(B) = 0.5. If A ⊆ B, then the values of conditional probabilities P(A|B) and P(B|A) are respectively

  3. If two dice are thrown and at least one the dice show 5, then the probability that the sum is 10 or more is

  4. If A and B are two events such that P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.4, then consider the following statements:

    1. P(A̅ ∪ B) = 0.9

    2. P(B̅ | A̅) = 0.6

    Which of the statements is / are correct? 

  5. For two mutually exclusive events A and B, P(A) = 0.2 and P (A̅ ∩ B) = 0.3. What is P (A|(A ∪ B)) equal to?

  6. Consider the following statements:

    1. If A and B are mutually exclusive events, then it is possible that P(A) = P(B) = 0.6.

    2. If A and B are any two events such that P(A|B) = 1, then P(B̅|A̅) = 1

    Which of the above statement is/are correct?
  7. If A, B, C are three events, then what is the probability that at least two of these events occur together?

  8. If 5 of a Company’s 10 delivery trucks do not meet emission standards and 3 of them are chosen for inspection, then what is the probability that none of the trucks chosen will meet emission standards?

  9. A problem is given to three students A, B and C whose probabilities of solving the problem are \(\frac{1}{2},\frac{3}{4}\) and \(\frac{1}{4}\)  respectively. What is the probability that the problem will be solved if they all solve the problem independently?

  10. Three groups of children contain 3 girls and 1 boy; 2 girls and 2 boys: 1 girl and 3 boys. One child is selected at random from each group. The probability that the three selected consist of 1 girl and 2 boys is


Important Questions from Conditional Probability

  1. Let A and B be two events such that \(P(\overline{A \cup B}) = \dfrac{1}{6}\) , P(A ∩ B) =  \(\dfrac{1}{4}\) and P(A̅) =  \(\dfrac{1}{4}\) , where A̅ stands for complement of event A. Then, events A and B are:

  2. A bike manufacturing factory has two plants P and Q. Plant P manufactures 60 percent of bikes and plant Q manufacture 40 percent. 80 percent of the bikes at plant P and 90 percent of the bikes at plant Q are rated of standard quality. A bike is chosen at random and is found to be of standard quality. What is the probability that it has come from plant P?

  3. A and B are two events such that A̅ and B̅ are mutually exclusive. If P(A) = 0.5 and P(B) = 0.6, then what is the value of P(A|B)?

  4. For two dependent events A and B, it is given that P(A) = 0.2 and P(B) = 0.5. If A ⊆ B, then the values of conditional probabilities P(A|B) and P(B|A) are respectively

  5. In a bulb factory, machines P, Q and R manufacture respectively 25%, 35% and 40% of the total. Of their output 5, 4 and 2 percent respectively are defective bulbs. A bulb is drawn at random and it is found to be defective. What is the probability that it was manufactured by machine Q?

Need Expert Advice?
Test Series
NDA img
Defence
NDA 2026 Mock Test Series (Latest Pattern)
503 Tests 1 Tests Free
1066 Attempts
4.6(137)
English, Hindi

Start Your Preparation with Prepp Mobile App

Download the app from Google Play & App Store
Download the app from Google Play & App Store
Prepp Mobile App