Question

List and appropriate sample space for this experiment. Lis the even a head is tossed and and even number is rolled. An experiment consists of tossing a coin, rollinng a diee and observing outcomes

Answer 1

As per given by the question,

There are given that,

Experiment consist of tossing a coin, rolling a diee.

Now,

For the appropriate sample of above experiment,

Now,

If coin is tossed, then the possible outcome is,

H or T

So,

The sample space of tossed coin is 2.

And,

If diee is rolled, then their possible outcom is,

1, 2, 3, 4, 5, or 6.

So,

The sample space of rolled diee is 6.

Now,

The even number is rolled in a diee is,

2, 4, and 6.

The probability of even number in diee is,

`\begin{gathered} P(\text{even number)= }(3)/(6) \\ =(1)/(2) \end{gathered}`

Now,

The number of head in a tossed coin is 1.

The probability of head in a tossed coin is,

`P(\text{head)}=(1)/(2)`

Then, the probability that getting even a head is tossed and even nuber is rolled,

`\begin{gathered} P(\text{even number)}* P(head)=(1)/(2)*(1)/(2) \\ =(1)/(4) \\ =0.25 \end{gathered}`

Hence, the sample space of tossed coin is 2, the sample space of rolling diee is 6, and the probability tha getting the even a head and even number is rolled is 0.25.