im doing an intensive maths course as a prerequisite to uni- but im finding 2nd week a little difficult. I cant keep up with all the formulas and everything. can someone explain how to work this out - do I use a tree diagram or a formula
Hello,
I tried the question so here is the solution(I could be wrong but here is what I did)
So this whole question is about binomial distribution because you have a sample and you are choosing people from it.
a) Using calculator(I used CAS) "4 people select 3 or more" meaning total number of sample is 4, you select 3 or 4 people from it that have the gene, probability that those people have the gene is 3/5. So using the calculator you select
binomial Cdf(as you have 3 or more people so its kind of an interval)
n=4, p=3/5, lower bound=3, upper bound=4(You can use the formula of biomial distribution but using calculator is faster)
This gives an answer of 0.4752.
b) this is conditional probability because of the phrase "given that". So the conditional probability has the formula of A intersection b divided by probability of B. Here A is the probability that "exactly 2" have the gene, and B is the probability that "at least 1" have the gene. So the intersection between those 2 is event A which is probability of having "exactly 2" divide that by the probability of having "at least 1".
Using your calculator:
For the numerator you use biomial pdf (bc of the phrase "exactly 2") thus n=4, p=3/5, X value=2 which gives an answer of 0.3456
For the denominator you use binomial cdf "bc of the phrase "at least 1" thus n=4, p=3/5, lower bound=1, upper bound=4 which gives an answer of 0.9744
Lastly divide A intersection B so 0.3456/0.9744 which gives 0.34568
Again not sure if I am right but that's my answer.