Question

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

a) {HH, HT, T1, T2, T3, T4, T5, T6}
b) {HH, HT, T1, T2, T3, T4, T5, T6, H1, H2, H3, H4, H5, H6}
c) {HH, HT, T1, T2, T3, T4, T5, T6, H1, H2, H3, H4, H5, H6, TH, TT}
d) {HH, HT, T1, T2, T3, T4, T5, T6, H1, H2, H3, H4, H5, H6, TH, TT, H}

Answer 1

The correct sample space for the given experiment is {HH, HT, T1, T2, T3, T4, T5, T6}, taking into account the conditional nature of the second part of the experiment.

Step-by-step explanation:

The correct sample space for the given experiment is {HH, HT, T1, T2, T3, T4, T5, T6}. This is because the experiment consists of two stages. The first stage is tossing a coin. If a head (H) occurs, the coin is tossed again, leading to the possibilities of HH (heads on both tosses) or HT (head on the first toss and tail on the second). If a tail (T) occurs on the first toss, the second stage is rolling a die, resulting in the outcomes T1, T2, T3, T4, T5, and T6, where the number represents the result on the die.

This sample space does not include outcomes such as H1, H2, H3, H4, H5, H6 nor TH, TT, or H, because there is no die roll after a first-toss head, and there is no second coin toss after a first-toss tail.