Question

In order to get a head at least once probability ~ 0.9, the minimum number of time a unbiased coin needs to be tossed is ______.

Options

• 3

• 4

• 5

• 6

Answer 1

In order to get a head at least once probability ~ 0.9, the minimum number of time a unbiased coin needs to be tossed is 4.

Explanation:

Let coin is tossed 'n' number of times.

Probability of getting head is p = `1/2`

∴ q = `1 - 1/2 = 1/2`

P(X ≥ 1) > `9/10`

∴ 1 - P(X < 1) > `9/10`

∴ `1 - (1/2)^"n" > 9/10`

∴ `(1/2)^"n" < 1/10`

∴ 10 < 2ⁿ

∴ n = 4 is the minimum value.