Question

An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the first toss, then a die is tossed once. Find the sample space.

Answer 1

Given: A coin is tossed and a die is rolled.

In the given experiment, coin is tossed and if the outcome is tail then, die will be rolled.

The possible outcome for coin is 2 = {H, T}

And, the possible outcome for die is 6 = {1, 2, 3, 4, 5, 6}

If the outcome for the coin is tail then sample space is S1= {(T, 1) (T, 2) (T, 3) (T, 4) (T, 5) (T, 6)}

If the outcome is head then the sample space is S2 = {(H, H) (H, T)}

So, the required outcome sample space is S = S1 ⋃ S2

S = {(T, 1) (T, 2) (T, 3) (T, 4) (T, 5) (T, 6) (H, H) (H, T)}

∴ The sample space for the given experiment is {(T, 1) (T, 2) (T, 3) (T, 4) (T, 5) (T, 6) (H, H) (H, T)}