Infinite trials?

Probability Level 3

Repeatedly toss a fair coin. What is the probability that the first head occurs on an even-numbered toss?


The answer is 0.33.

Rohit Udaiwal by Rohit Udaiwal , 20, India

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2 solutions

Let the probability of the first head occurring on the n n th toss be P n P_{n} . Then, we get P n = 1 2 n P_{n}=\frac{1}{2^{n}}

So now, we need to find the value of S = ∑ n = 1 ∞ 1 2 2 n S=\sum _{n=1}^{\infty}\frac{1}{2^{2n}}

S = 1 4 + 1 4 ⋅ S S=\dfrac{1}{4}+\dfrac{1}{4}\cdot S

S = 1 3 S=\dfrac{1}{3} , so the answer is 0.333.....

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Prince Loomba
Jan 24, 2016

Gemeral answer if p is probability of head: 1-p/2-p.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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