Question

A probability experiment is conducted in which the sample space of the experiment is

Sequals=StartSet 6 comma 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 EndSet{6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}​,

event

Upper F equals StartSet 10 comma 11 comma 12 comma 13 comma 14 comma 15 EndSetF={10, 11, 12, 13, 14, 15}​,

and event

Upper G equals StartSet 14 comma 15 comma 16 comma 17 EndSetG={14, 15, 16, 17}.

Assume that each outcome is equally likely. List the outcomes in F or G. Find

Upper P left parenthesis Upper F or Upper G right parenthesisP(F or G)

by counting the number of outcomes in F or G. Determine

Upper P left parenthesis Upper F or Upper G right parenthesisP(F or G)

using the general addition rule.

Answer 1

The sample space is S= {6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}.

The event F= {10, 11, 12, 13, 14, 15}​.

The event G= {14, 15, 16, 17}.

Then the outcomes in (F or G) = {10, 11, 12, 13, 14, 15, 16, 17}

Counting number of outcomes:

Let n(A) be the cardinality of set A.

Then

Here n(S) = 12 and n(F or G) = 8.

So

Using Addition Rule:

We have,

And (F and G) = {14, 15}

So,

Under addition rule, we know

Using the above values,

So for both the approach we get that P(F or G) = 0.67.

Please Upvote if the answer solves your problem.