Question

A coin is tossed three times. Use this information to solve these problems.1) List the sample space.2) Find the probability of tossing heads exactly twice.3) Find the probability of tossing tails at least twice.

Answer 1

1) sample space = {HHH, HHT, HTH, THH, THT, TTH, HTT, TTT}

2) pr(tossing heads exactly twice) =
`(3)/(8)`

3) pr(tossing tails at least twice) =
`(1)/(2)`

Explanation:

In tossing a coin three times, the sample space is the possible outcomes for the number of toss.

So that for the question,

1) The sample space = {HHH, HHT, HTH, THH, THT, TTH, HTT, TTT}

The total number of possible outcome is 8.

2) pr(tossing heads exactly twice) =
`(numner of outcome with exactly two heads)/(total number of outcome)`

=
`(3)/(8)`

3) pr(tossing tails at least twice) =
`(number of outcome with at least two tails)/(total number of outcome)`

=
`(4)/(8)`

=
`(1)/(2)`