A boy tosses fair coin 3 times. If he gets rs.2x for x heads then his expected gain equals to rs.....
Answers
Expected gain = Rs 3 A boy tosses fair coin 3 times. If he gets rs.2x for x heads
Step-by-step explanation:
Probability of head p = 1/2
probability of not head q = 1 - 1/2 = 1/2
P(0) = ³C₀(1/2)⁰(1/2)³ = 1/8
P(1) = ³C₁(1/2)¹(1/2)² = 3/8
P(2) = ³C₂(1/2)²(1/2)¹ = 3/8
P(3) = ³C₃(1/2)³(1/2)⁰ = 1/8
Number of Heads Gain Probability Net Gain
0 0 1/8 0
1 2 3/8 3/4
2 4 3/8 3/2
3 6 1/8 3/4
Expected gain = 0 + 3/4 + 3/2 + 3/4
= 3
Expected gain = Rs 3
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