A probability experiment is conducted in which the sample sp

A probability experiment is conducted in which the sample space of the experiement is S=(1,2,3,4,5,6,7,8,9,10,11,12), event F=(6,7,8) and event G=(10,11,12). Assume that each outcome is equally likely. List the outcomes in F or G. Find P (F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.

Solution

a)

List the outcomes in F or G.

F or G = all elements in F or G = {6,7,8,10,11,12} [answer]

b)

Find P (F or G) by counting the number of outcomes in F or G.

There are 6 elements in F or G, and 12 elements in S. Thus,

P(F or G) = 6/12 = 0.5 [answer]

c)

Determine P(F or G) using the general addition rule.

P(F or G) = [n(F) + n(G) - n(F and G)] / n(S)

As F and G = { }, n(F and G) = 0. Thus,

P(F or G) = [3 + 3 - 0] / 12 = 0.5 [answer]