Question

A probability experiment is conducted in which the sample space of the experiment is S={7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}. Let event E={9, 10, 11, 12, 13, 14, 15, 16}, 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

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

`P(F\ or\ G) = (2)/(3)`

Explanation:

Given

`S= \{7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18\}`

`E=\{9, 10, 11, 12, 13, 14, 15, 16\}`

`F=\{5, 6, 7, 8, 9\}`

`G=\{9, 10, 11, 12\}`

`H=\{2, 3, 4\}.`

Solving (a): Outcomes of F or G

F or G is the list of items in F, G or F and G.

So:

`F=\{5, 6, 7, 8, 9\}`

`G=\{9, 10, 11, 12\}`

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

Solving (b): P(F or G)

The general addition rule is:

`P(F\ or\ G) = P(F) + P(G) - P(F\ and\ G)`

Where:

`P(F) = (n(F))/(n(S)) = (5)/(12)`

`P(G) = (n(G))/(n(S)) = (4)/(12)`

`P(F\ and\ G) = (n(F\ and\ G))/(n(S))`

`F\ and\ G = \{9\}`

So:

`P(F\ and\ G) = (1)/(12)`

`P(F\ or\ G) = P(F) + P(G) - P(F\ and\ G)`

`P(F\ or\ G) = (5)/(12) + (4)/(12) - (1)/(12)`

`P(F\ or\ G) = (5+4-1)/(12)`

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

`P(F\ or\ G) = (2)/(3)`