l binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.

n=11 p=0.4 x

Question

l binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.

n=11   p=0.4  x<_4


The probability of x<_4 successes is___.
(Round to four decimal places as needed.)

anonymous · Answer

attachment

kropot72 · Answer

$$P(4\ successes)=11C4\times (0.4)^{4}\times (0.6)^{7}$$
Now you need to find P(3 successes), P(2 successes), P(1 success) and P(0 successes) and add these five values of probability to find the required probability.

anonymous · Answer

what's the formula for that?

kropot72 · Answer

If there are n trials with a probability p of success on each trial then the probability of exactly x successes is
$$P(X=x)=\left(\begin{matrix}n \ x\end{matrix}\right)p ^{x}(1-p)^{n-x}$$
You need to uses the formula five times and add the five results.

anonymous · Answer

i thought it was 4?

kropot72 · Answer

You need to find P(4 successes), P(3 successes), P(2 successes), P(1 success) and P(0 successes) and add these five values of probability to find the required probability.