3. A probability experiment is conducted in which the sample space of the experi

Question

3. A probability experiment is conducted in which the sample space of the experiment is S= {2,3,4,5,6,7,8,9,10,11,12,13}, event F={4,5,6,7,8}, and event G={8,9,10,11}. Assume that each outcome is 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.

List the outcomes in F or G. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

MULTIPLE CHOICE

A. F or G= {?}

(Use a comma to separate answers as needed.)

B. F or G= {}

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

P(F or G)= ?

(Type an integer or a decimal rounded to three decimal places as needed.)

Determine P (F or G) using the general addition rule. Select the correct choice below and fill in any answer boxes within your choice. (Type the terms of your expression in the same order as they appear in the original expression. Round to three decimal places as needed.)

MULTIPLE CHOICE

A. P (F or G)= ? + ?- ? = ?

B. P (F or G) = ? + ? = ?

4. Find the probability of the indicated event if P(E) = 0.20 and P(F)= 0.40.

Find P(E or F) if P(E and F)= 0.15

P (E or F)= ? (Simplify your answer.)

6. Suppose that events E and F are independent, P(E)= 0.6, and P(F)=0.9. What is the P(E and F)?

The probability P(E and F) is ? (Type an integer or a decimal)

Explanation / Answer

Question 3: Here we are given that:

S= {2,3,4,5,6,7,8,9,10,11,12,13}, event F={4,5,6,7,8}, and event G={8,9,10,11}

a) Method by counting:

F or G is the event that contains:

F or G = { 4, 5, 6, 7, 8, 9, 10, 11 }

Therefore there are 8 outcomes here out of the total 12 outcomes. Therefore the required probability is computed as:

P(F or G) = 8/12 = 0.6667

Therefore 0.6667 is the required probability here.

b) Now using law of addition we have here:

P(F) = 5/12 and P(G) = (4/12) and also P(F and G) = 1/12 because only 1 element is common here.

Therefore, using addition law we get:

P(F or G) = P(F) + P(G) - P(F and G) = (5/12) + (4/12) - (1/12) = 8/12 = 0.6667

Therefore 0.6667 is the required probability here.

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