Question

On tossing three coins simultaneously, find the probability of getting atleast a head and a tail.

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $\frac{2}{3}$

Answer 1

The correct option is C

$\frac{3}{4}$

Given,

Sample space for tossing a coin three times = S{(H,H,H) , (H,H,T) , (H,T,H) , (H,T,T) , (T,H,H) , (T,H,T) , (T,T,H) , (T,T,T)}

$\Rightarrow$Total number of outcomes = 8

Out of 8 outcomes, the favourable outcomes are - (H,H,T) , (H,T,H) , (H,T,T) , (T,H,H) , (T,H,T) , (T,T,H)

Number of favourable outcomes = 6

Probability of an event, P(E)$=\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$

$\Rightarrow$ P(E) =$\frac{6}{8}=\frac{3}{4}$

Therefore, the probability of getting atleast a head and a tail is $\frac{3}{4}$ .