Question

A probability experiment is conducted in which the sample space of the experiment is S={1,2,3,4,5,6,7,8,9,10,11,12}. Let event E={3,4,5,6,7,8}. Assume each outcome is equally likely. List the outcomes in Ec. Find P(Ec).The outcomes of Ec are {_____}P(Ec)=

Answer 1

This list of all the outcome of
`E^c` is
`E^c = \{ 1,2,9,10,11,12,\}`

`P(E^c ) = 0.5`

Explanation:

From the question we are told that

The sample sample space is
`S = \{ 1,2,3,4,5,6,7,8,9,10,11,12 \}`

The number of elements in the sample space is
`n = 12`

The event is
`E = \{ 3,4,5,6,7,8 \}`

The number of outcomes in the Event is
`n_e = 6`

The objective in to obtain
`P(E^c)`

Now
`E^c` is the compliment of E and number of elements in
`E^c` ican be mathematically evaluated as

`nE^c = n - n_e`

substituting values

`E^c = 12-6`

`E^c = 6`

This list of all the outcomes of
`E^c` is

`E^c = \{ 1,2,9,10,11,12,\}`

Generally
`P(E^c )` which is the probability of
`E^c` is mathematically evaluated as

`P(E^c ) = (nE^c)/(n)`

substituting values

`P(E^c ) = (6)/(12)`

`P(E^c ) = 0.5`