Multiple choice

In order to get atleast once a head with probability $\ge 0.9$, the number of times a coin needs to be tossed is

  1. $3$
  2. $4$
  3. $5$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Probability of getting at least one head in n tosses is 1 - (1/2)^n. We need 1 - (1/2)^n >= 0.9, which means (1/2)^n <= 0.1. For n=3, 1/8 = 0.125. For n=4, 1/16 = 0.0625. Thus, 4 tosses are required.

AI explanation

The probability of not getting a head in n tosses is (1/2)^n, so the probability of getting at least one head is 1 - (1/2)^n. Setting this greater than or equal to 0.9 gives 0.1 greater than or equal to (1/2)^n. Testing n = 4, we get (1/2)^4 = 1/16 = 0.0625, which is less than 0.1; whereas for n = 3, (1/2)^3 = 0.125, which is not less than 0.1. Therefore, the minimum number of tosses required is 4.

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