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

Answer:

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

$P(F\ or\ G) = \frac{2}{3}$

Step-by-step 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:

$P(F) = \frac{n(F)}{n(S)} = \frac{5}{12}$

$P(G) = \frac{n(G)}{n(S)} = \frac{4}{12}$

$P(F\ and\ G) = \frac{n(F\ and\ G)}{n(S)}$

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

So:

$P(F\ and\ G) = \frac{1}{12}$

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

$P(F\ or\ G) = \frac{5}{12} + \frac{4}{12} - \frac{1}{12}$

$P(F\ or\ G) = \frac{5+4-1}{12}$

$P(F\ or\ G) = \frac{8}{12}$

$P(F\ or\ G) = \frac{2}{3}$