Question

A coin is tossed $n$ times. The maximum value of $n$ such that the probability of getting no head is greater than $1/16$ is

• A. $4$
• B. $3$
• C. $5$
• D. $2$

Answer 1

Answer: (B)

$3$

When you toss a coin one time, chances of no heads is 1/2.

When you tolls 2 times, no head chances = 1 /4 (You have 4 options, TT, TH, HT or HH)

=> with n tosses, chances of no heads is ${\left(1/2\right)}^n$

${\left(1/2\right)}^n$) > (1/16)

=> ${\left(2\right)}^n$ < 16 (when fraction inequality changes the sign reverses)

=> n < 4.

So answer is tossing 3 times, you will have more probability of no heads.