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={2, 3, 4, 5, 6, 7}, event F={5, 6, 7, 8, 9}, event G={9, 10, 11, 12}, and event H={2, 3, 4}. Assume that each outcome is equally likely. List the outcome s in For G. Now find P( For G) by counting the numb er of outcomes in For G. Determine P (For G ) using the General Addition Rule.

Answer 1

The answer is "
`\bold{(2)/(3)}`"

Explanation:

Given set:

`\to F \ or\ G = \{ 5,6,7,8,9,10,11,12\}`

In the above-given set, there are 8 elements and 12 possible outcomes so, the equation is:

`\to P( F\ or \ G) = (8)/(12)`

`= (2)/(3)`

by using the general addition Rule:

`\to P(F \cup G) = P(F) +P(G)- P(F \cap G)`

`=(5)/(12)+(4)/(12)- P(E \cap H)\\\\=(6)/(12)+(3)/(12)- (1)/(12)\\\\=(6+3-1)/(12)\\\\=(8)/(12)\\\\=(2)/(3)\\\\`