Question

A coin is tossed. If it shows a tail, we draw a ball from a box containing 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

Answer 1

The sample space for this experiment consists of all the possible outcomes at each step: tail and draw a red ball, tail and draw a black ball, head and roll a 1, head and roll a 2, head and roll a 3, head and roll a 4, head and roll a 5, and head and roll a 6.

Step-by-step explanation:

The sample space for this experiment can be determined by considering all the possible outcomes at each step.

If the coin shows a tail, we draw a ball from the box containing 2 red and 3 black balls. So the possible outcomes are:

Tail and draw a red ball

Tail and draw a black ball

If the coin shows a head, we throw a die. So the possible outcomes are:

Head and roll a 1

Head and roll a 2

Head and roll a 3

Head and roll a 4

Head and roll a 5

Head and roll a 6

Combining the outcomes from both the coin toss and the subsequent events, the sample space for this experiment is:

Tail and draw a red ball

Tail and draw a black ball

Head and roll a 1

Head and roll a 2

Head and roll a 3

Head and roll a 4

Head and roll a 5

Head and roll a 6