A group of students from BIOL 283 is working on their research project. They wan

Question

A group of students from BIOL 283 is working on their research project. They want to see if mice use olfaction (smell) or sight in selecting food. They design an interesting experiment where they paint little wooden pegs yellow and brown and use food coloring to color food pellets either yellow or brown. After mice become habituated to one color of food pellet, they are presented a choice between a food pellet of opposite color or a wooden peg of the same color. The students record the choice the mice make.

At one point, a bowl of 20 pegs and a bowl of 20 pellets are simultaneously knocked on the floor, mixing them together. Because the students were so good at making the pegs look like pellets, they must use a dissecting scope to look at each under high magnification,one by one, to reorganize the two bowls. What is the probability that the first four randomly selected food bits are actually food pellets and not wooden pegs? a.) 4.54% b.) 10% c.) 0% d.) 5.30% e.) 6.25%

Explanation / Answer

There are 40 pellets in all, 20 are real food.

We choose 4 of them.

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    40      
K = number of successes in the population =    20      
n = sample size =    4      
x = number of successes in the sample =    4      
          
Thus,          
          
P(   4   ) =    0.053014553 = 5.30% [ANSWER, D]

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