Question

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.

Answer 1

Answer:

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

Answer 2

Answer:

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!