A coin is tossed twice. If the second throw results in head, then a die is thrown. Describe the sample space of the experiment.

Open in App

Solution

Step 1: Find the sample space for tossing a coin twice:
Sample space for throwing a coin twice,
$n (S) = {(numberofpossibleoutcomesoftossingacoin)}^{numberofcoinstossed} n (S) = {(2)}^{2} n (S) = 4$
Thus, the sample space of tossing a coin twice will be,
$S_{1} = {H H, H T, T H, T T}$
Step 2: Find the sample space if the second throw results in head, then a die is thrown:
Let $S_{2}$ be the number of events when the second throw results in head i.e., ${H H, T H}$ , then a die is thrown will be,
Thus, the sample space will be,
$S_{2} = {(H H, 1), (H H, 2), (H H, 3), (H H, 4), (H H, 5), (H H, 6), (T H, 1), (T H, 2) (T H, 3), (T H, 4), (T H, 5), (T H, 6)}$
Step 3: Find the total sample space:
The total sample space $S = S_{1} \cup S_{2}$ .
Therefore, the total sample space for the given experiment will be,
$S = (H, T), (T T), (H H, 1), (H H, 2), (H H, 3), (H H, 4), (H H, 5), (H H, 6), (T H, 1), (T H, 2), (T H, 3), (T H, 4), (T H, 5), (T H, 6)$
Final answer:
Hence, the sample space of the experiment is $S = (H, T), (T T), (H H, 1), (H H, 2), (H H, 3), (H H, 4), (H H, 5), (H H, 6), (T H, 1), (T H, 2), (T H, 3), (T H, 4), (T H, 5), (T H, 6)$ .

Suggest Corrections

Similar questions

A coin is tossed twice. If the second throw results in a tail, a die is thrown. Deseri the sample space for this experiment.

Join BYJU'S Learning Program