Question

An experiment consists of flipping a coin and then flipping it a second time if head occurs. if a tail occurs on the first flip, then a six-faced die is tossed once. assuming that the outcomes are equally likely, what is the probability of getting one head and tail?

• A. $\frac{1}{4}$
• B. $\frac{1}{36}$
• C. $\frac{1}{6}$
• D. $\frac{1}{8}$

Answer 1

The correct option is D

$\frac{1}{8}$

Finding the probability:

If a coin tossed there can be either head or tail .

Let head denoted by H & tail denoted by T.

Similarly, if a die is rolled possible outcomes are $1,2,3,4,5\&6$

If head comes tossed a coin again possible outcomes are$=\left\{HH,HT\right\}$

If tail comes rolled a die possible outcomes are $\left\{T1,T2,T3,T4,T5,T6\right\}$

sample space 8 associated with the experiment is

$S=\left\{HH,HT,T1,T2,T3,T4,T5,T6\right\}.$

Probability of getting one head and one tail $=p\left(HT\right)=\frac{1}{8}$

Hence option(D) is correct.