Probability — Questions & Answers

Sample questions from Probability

1. Q1. For X ~ B(8, 1/2), the probability P(X = 3) is:

   • A.7/32✓
   • B.28/128
   • C.3/8
   • D.7/64
   Solution

   P(X = 3) = C(8,3)(1/2)^8 = 56/256 = 7/32.

2. Q2. A circuit contains three switches in series, each functioning independently with probability 0.9. The probability that current flows through the circuit is:

   • A.0.9
   • B.0.999
   • C.0.729✓
   • D.0.271
   Solution

   For a series circuit all three must function: 0.9^3 = 0.729.

3. Q3. Events A and B satisfy P(A) = 3/8, P(B) = 5/8 and P(A ∪ B) = 3/4. The value of P(A | B) is:

   • A.1/4
   • B.2/5
   • C.3/5✓
   • D.5/8
   Solution

   P(A ∩ B) = 3/8 + 5/8 - 3/4 = 1/4. Then P(A ∩ B) = P(B) - P(A ∩ B) = 5/8 - 1/4 = 3/8 and P(A | B) = (3/8)/(5/8) = 3/5.

4. Q4. Three independent events A, B, C have probabilities 1/2, 1/3 and 1/5 respectively. The probability that exactly two of them occur is:

   • A.11/15
   • B.1/30
   • C.7/30✓
   • D.4/15
   Solution

   P = (1/2)(1/3)(4/5) + (1/2)(2/3)(1/5) + (1/2)(1/3)(1/5) = 4/30 + 2/30 + 1/30 = 7/30.

5. Q5. Two dice are thrown and it is known that at least one of them shows a 3. The probability that the sum of the numbers is odd is:

   • A.1/2
   • B.6/11✓
   • C.5/11
   • D.6/36
   Solution

   At least one 3 gives 11 outcomes. The sum is odd when the other die is even: (3,2),(3,4),(3,6),(2,3),(4,3),(6,3) — 6 outcomes, so 6/11.

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