Cristian M. answered • 08/10/20
MS Statistics Graduate with 5+ Years of Tutoring Experience
Question:
Do you have Snapchat?
Freq Yes No Total
Males 17 23 40
Females 20 40 60
Total 37 63 100
(a) Find P(𝑀/𝑌)
(b) Find 𝑃(𝑁|𝐹)
(c) Find 𝑃(𝑀𝑎𝑙𝑒 𝑜𝑟 𝑛𝑜)
Answer:
a) Given that someone said yes, what is the probability that they are male? First, let's reduce the sample space. We won't look at all 100 people for this. We're interested in the ones that said yes, so 37 people. How many of those yes-people were male? 17. So P(𝑀/𝑌) = 17/37.
b) Given that someone is a female, what is the probability that they said no? First, let's reduce the sample space. We won't look at all 100 people for this. We're interested in the females, so 60 people. How many of those females said no? 40. So 𝑃(𝑁|𝐹) = 40/60, or 2/3.
c) What is the probability that a respondent was male or said no? This question will consider all 100 people. First, find the probability of being a male respondent, then find the probability of being a respondent that said no. Finally, remove the probability of being male and having said no.
That is, P(male) + P(no) - P(male and no).
Males make up 40/100 of the respondents. P(male) = 40/100.
No-sayers (er, naysayers?) make up 63/100 of the respondents. P(no) = 63/100.
People who were male and said no make up 23/100 of the respondents. P(male and no) = 23/100.
So (40/100) + (63/100) - (23/100) = 80/100.
P(male or no) = 80/100, or 4/5.
