1. In a group of people, some are in favor of a tax increase on rich people (F)
ID: 2946095 • Letter: 1
Question
1. In a group of people, some are in favor of a tax increase on rich people (F) and others are against it (A). Three persons are selected at random from this group and their opinions in favor (F) or against (A) raising such taxes are noted. a) How many total outcomes are possible? (Hint: you can use m.n.k formula here) b) Write down the sample space. c) "At least one person is in favor" - Is this a simple event or compound event? Explain your answer. d) Both person are against tax increase - Is this a simple event or compound event? Explain your answer. e) Assume another option is added where people can have “no opinion (N)" So now, people can either be in favor (F), against (A) or have no opinion (N). How many total outcome will be there in sample space? (Hint: you can use m.n.k formula here, no need to write the entire sample Space 2. In a class there are 40 students in total, among which 20 are male and 20 are female. If one student is randomly selected, a) What is the probability that the student will be male P(M)? b) What is the probability that the student will be female P(F)? c) Are being male or female equally likely outcomes? Explain your answer. d) Will they still be equally likely event if number of female student becomes 10 and number of male student becomes 30? Explain your answer.Explanation / Answer
a) Each person can opt for either F or A . So each person has two options .
So total no. of outcomes for three persons = 2*2*2 = 8
b) Sample space includes all the possible outcomes of a experiment .
they are : FFF, FFA, FAF , FAA , AFF, AFA, AAF , AAA
c) A compound event is one in which there is more than one possible outcome. so , one person can be in favour or two or all three can be in favour . So more than one possible outcome is possible . hence it is a compound event.
d) It is also a compound event as the third person can be in favour or against . so there are two possible outcomes.
e) each person has three choices: F , A or N.
So total no. of outcomes = 3*3*3 =27
2)
a) no. of males = 20
total students = 40
so P(M) = 20/40 = 0.5
b) no. of females = 20
total students = 40
so P(F) = 20/40 = 0.5
c) sas from above the P(F) = P(M) m they are equally likely outcomes . Also since the no. of males is equal to that of female ,it has to be equally likely outcomes.
d) NO, since their nos. are not equal .
P(M) = 30/40 =0.75
P(F) =10/40 = 0.25
P(F) IS NOT EQUAL TO P(M) .
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.