DXC Technology Probability Questions and Answers Quiz-1

Answer: a
Explanation: P(A ∩ B) = P(A – (A ∩ B))
= P(A) – P(A ∩ B)
= 0.6 – 0.2 Using P(A) = 1 – P(A)
= 0.4.

Explanation:
Let A be the event of A solving the problem
Let B be the event of B solving the problem
Let C be the event of C solving the problem
Given P(a) = ¹⁄₂, P(~B) = ¹⁄₄ and P(A ∪ B ∪ C) = 63/64

We know P(A ∪ B ∪ C) = 1 – P(A ∪ B ∪ C)

= 1 – P(A ∩ B ∩ C)

= 1 – P(A) P(B) P(C)

Let P(C) = p
ie ⁶³⁄₆₄ = 1 – (¹⁄₂)(¹⁄₄)(p)

= 1 – ^p⁄₈
⇒ P =1/8 = P(C)
⇒P(C) = 1 – P = 1 – ¹⁄₈ = ⁷⁄₈.

Answer: c
Explanation:
For independent events,
P(A ∩ B) = P(A) P(B)
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
= P(A) + P(B) – P(A) P(B)
= ¹⁄₅ + P (¹⁄₅)P
⇒ ¹⁄₂ = ¹⁄₅ + ⁴⁄₅P
⇒ P= ³⁄₈.

Answer: a
Explanation: As A and B are mutually exclusive we have

Answer: a
Explanation: For independent events,
P(A /~B) = P(a) = 0.2.

Answer: b
Explanation:
P(A ∩ B) = 0 as (A ∩ B) = ∅
But P(A ∩ B) ≠ 0 , as P(a) > 0 and P(b) > 0
P(A ∩ B) = P(A) P(B), for independent events.