Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases. suppose 15 samples are studied, and they can be considered to be independent for mutation. determine the following probabilities. (a) no samples are mutated. (b) at most one sample is mutated. (c) more than half the samples are mutated.

C) At most one sample is mutated

Step-by-step explanation:

If there are 15 samples, it means that 15 is the total (100%) of samples. Then, if we know that there is a chance that 3% are mutated, then we calculate the 3% of 15:

This means that at most one sample is mutated, as this result is not zero (we discard answer A), and 0.45 is not more than half of the samples.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb