A probability experiment is conducted in which the sample space of the experiment is Sequals=StartSet 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 comma 19 comma 20 EndSet{9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} , event Upper F equals StartSet 9 comma 10 comma 11 comma 12 comma 13 EndSetF={9, 10, 11, 12, 13} , and event Upper G equals StartSet 13 comma 14 comma 15 comma 16 EndSetG={13, 14, 15, 16}. Assume that each outcome is equally likely. List the outcomes in F or G. Find Upper P (Upper F or Upper G) P (F or G) by counting the number of outcomes in F or G. Determine Upper P (Upper F or Upper G) P (F or G) using the general addition rule.

From both approaches P (F or G) = 0.667

Step-by-step explanation:

P (F or G) = ?

F={9, 10, 11, 12, 13}

G={13,14,15,16}

Finding P (F or G) by counting outcomes in F or G

F or G={9, 10, 11, 12, 13}or {13,14,15,16}

F or G={9, 10, 11, 12,13,14,15,16}

number of outcomes in F or G=n (F or G) = 8

S={9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

number of outcomes in S=n (S) = 12

P (F or G) = n (F or G) / n (S)

P (F or G) = 8/12

P (F or G) = 0.667

Finding P (F or G) by addition rule

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

F={9, 10, 11, 12, 13}

number of outcomes in F=n (F) = 5

P (F) = n (F) / n (S)

P (F) = 5/12

P (F) = 0.417

G={13,14,15,16}

number of outcomes in G=n (G) = 4

P (G) = n (G) / n (S)

P (G) = 4/12

P (G) = 0.333

F and G={9, 10, 11, 12, 13}and {13,14,15,16}

F and G={13}

number of outcomes in F and G=n (F and G) = 1

P (F and G) = n (F and G) / n (S)

P (F and G) = 1/12

P (F and G) = 0.083

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

P (F or G) = 0.417+0.333-0.083

P (F or G) = 0.667

8/12

Step by step explanation:

The outcomes are the elements in the sample space S={9,10,11,12,13,14,15,16,17,18,19,20}

There are 12 outcomes in this sample space. Since each outcome is equally likely (has equal chance of occurring) then each outcome's probability is 1/12.

(A) the list of outcomes in (F or G) are: (F or G) = {9,10,11,12,13,14,15,16}

(B) P (F or G) = P{9,10,11, ...,16}

By counting the number of outcomes in (F or G), P (F or G) = 8/12

as there are 8 outcomes in (F or G) and 12 total outcomes in the sample space.

(C) Using addition rule,

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

P (F) = (1/12 for the outcome 9) + (1/12 for the outcome 10) + (1/12 for the outcome 11) + (1/12 for the outcome 12) + (1/12 for the outcome 13)

P (F) = 5/12

P (G) = 4/12

P (F and G) = probability of having the outcome '13' = 1/12

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

Kudos!