Question

If the probability is 0.85 that a fully charged digital camera battery will take 150 or more
pictures, find the probabilities that among 18 such batteries-

Answer 1

Full question (please post this next time): If the probability is 0.85 that a fully charged digital camera battery will take 150 or more pictures, find the probabilities that among 18 such batteries

a) 16 will take 150 pictures or more;
b) At least 14 will take 150 pictures or more;
c) At most 2 will not take 150 pictures or more.

Note: this is NOT a multiple choice question. It is asking for three separate calculations for scenarios a b and c.

Answer 2

We have a series of independent events in which each instance of the event only has two possibilities (either the camera battery will take 150+ pictures, or not). Therefore, this is a binomial distribution and thus we can use the binomial distribution formula:

\[P(x)=\left(\begin{matrix}n \\ x\end{matrix}\right)p^{x}q^{n-x}\]
where P(x) is the probability of "x" number of "successful" outcomes, n is the total number of trials, p is the probability of "success" and q is the probability of "failure. in our case, we can define "success" as a camera being able to take 150+ pictures and q the probability of *not* being able to take 150 pictures. n is the total number of trials. Recall that
\[\left(\begin{matrix}n \\ x\end{matrix}\right)\]means the combination nCx.

starting with scenario a) 16 will take 150 pictures or more
the total number of batteries is 18, so n = 18
for 16 cameras being able to take 150+ pictures, x = 16
p = the probability of a camera being able to take 150 pictures (given in the problem as 0.85)
q = the probability of *not* being able to take 150 pictures (1 - p)

plug in the appropriate quantities and evaluate.

Answer 3

for b) repeat the same logic. for "at least" 14 cameras, the x values would have to be 15, 16, 17, and 18, so you would repeat the calculation for each of these x values and add the probabilities.

for c) for "at most" 2 the appropriate x values would be x = 0, 1, and 2, repeat the same logic as part b)