Would anyone know how to compute the answer to the following quesiton(s). The answer to these questions are given in the textbook but i am having difficulty figuring out how they were obtained.
A geneticist has bred three different strains of fruitfly. In her lab, the geneticist currently has 8 strain flies, 6 strain B flies, and 4 strain C flies. Within each strain, the flies are genetically and phenotypically identical.
a) if the geneticist randomly seletcs 4 flies, what is the probability that none of them are strain B?
b) if the geneticist randomly selects 4 flies, what is the probability that at least 3 of them are strain A?
c) the geneticist wishes to randomly select 2 flies from each strain for an experiment. In how many ways can this be accomplished?
d) For another experiment, the geneticist will randomly select flies for 3 experiements. The first experiment requires 4 flies, the second and third experiments each require 3 other flies. If the assignment of flies to the 3 experiments is done randomly, what is the probability that each experiment gets exactly 2 strain A flies?
For the first question think of it this way:
When selecting the first fly the probability it is not of strain B is 12/18.
Now if you are to select another fly that isn't in strain B the chances of that are 11/17 (since the number of non-strain B flies is reduced as well as the total number of flies). The next is 10/16 and the probability for the last fly is 9/15. To get the probability of all these events occurring you multipy them together to get (12*11*10*9)/(18*17*16*15) = 0.162
If you look through your textbook you might see some different notation involving combinatorics and factorials (which you should probably be using) but they accomplish exactly what I have done above.
Don't have time to help you with the others but just try to think along the same lines. And learn how to use the notation in the textbook.
i figured out the answers