An experiment on the probability is carried out, in which the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Let event

Question

An experiment on the probability is carried out, in which the sample space of the experiment is
$S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 .$
Let event $E = 2, 3, 4, 5, 6, 7, e v e n t$
$F = 5, 6, 7, 8, 9, e v e n t G = 9, 10, 11, 12, a n d e v e n t H = 2, 3, 4$ .
Assume that each outcome is equally likely. List the outcome s in For G.
Now find P( For G) by counting the number of outcomes in For G.
Determine P (For G ) using the General Addition Rule.

Answer 1

Step 1
$F o r G = 5, 6, 7, 8, 9, 10, 11, 12$
Step 2
The set above has 8 elements, there are 12 possible outcomes, therefore
$P (F o r G) = \frac{8}{12} = \frac{2}{3}$
Using the General Addition Rule gives:
$P (F \cup G) = P (F) + P (G) - P (F \cap G)$
$P (F \cup G) = \frac{5}{2} + \frac{4}{12} - P (E \cap H)$
$P (F \cup G) = \frac{6}{12} + \frac{3}{12} - \frac{1}{12}$
$P (F \cup G) = \frac{8}{12} - \frac{2}{3}$

An experiment on the probability is carried out, in which the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Let event

Want to know more about Polynomial arithmetic?

Expert Answer

Not exactly what you’re looking for?

Relevant Questions