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 li…

Question

asked Apr 11, 2021 11.7k views

1 Answer

Patches · Answer 1 · 2021-04-17T23:26:05+0000

Answer:

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