ProbabilitymediumPYQ · JEE Main · 5 Apr 2026 · Shift 2 (Afternoon)Free

Probability: Players Selected Captain Probabilities Respectively Captain (JEE Main 2026)

JEE Maths question with a full step-by-step solution.

Question
Players AA and BB are selected as captain with probabilities 0.60.6 and 0.40.4 respectively. If AA is captain, the team wins with probability 0.80.8; if BB is captain, the team wins with probability 0.70.7. Then the probability that the team wins is:
A0.740.74
B0.760.76correct
C0.720.72
D0.780.78
Solution
Step 1: Identify the events and apply the Total Probability Theorem Let WW denote the event of winning. With P(A)=0.6P(A)=0.6, P(B)=0.4P(B)=0.4:
P(W)=P(A)⋅P(W∣A)+P(B)⋅P(W∣B)P(W) = P(A)\cdot P(W\mid A) + P(B)\cdot P(W\mid B)
 Step 2: Substitute the given values
P(W)=(0.6)(0.8)+(0.4)(0.7)=0.48+0.28=0.76P(W) = (0.6)(0.8) + (0.4)(0.7) = 0.48 + 0.28 = 0.76
 Answer: (2)
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