Multiple choice

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

  1. 1/3

  2. 1/2

  3. 2/3

  4. 3/4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of getting a head on the first toss is 1/2, on the third is (1/2)^3, on the fifth is (1/2)^5, and so on. This is a geometric series with first term a = 1/2 and common ratio r = 1/4. The sum is a/(1-r) = (1/2)/(1 - 1/4) = (1/2)/(3/4) = 2/3.

AI explanation

The probability of the first head appearing on an odd-numbered toss is the sum of the geometric progression 1/2 + 1/8 + 1/32. Using the infinite geometric series sum formula with first term 1/2 and common ratio 1/4, the sum is (1/2) divided by (1 minus 1/4). This calculates to 2/3.

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