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

Answer:

The answer is " $\bold{\frac{2}{3}}$"

Step-by-step 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:

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

                      $= \frac{2}{3}$

by using the general addition Rule:

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

                    $=\frac{5}{12}+\frac{4}{12}- P(E \cap H)\\\\=\frac{6}{12}+\frac{3}{12}- \frac{1}{12}\\\\=\frac{6+3-1}{12}\\\\=\frac{8}{12}\\\\=\frac{2}{3}$