You are performing four independent Bernoulli trials with p = 0.4 and q = 0.6. Calculate the
probability of no successes.

Question

You are performing four independent Bernoulli trials with p = 0.4 and q = 0.6. Calculate the
probability of no successes.

kropot72 · Answer

$$P(0\ successes)=(0.6)^{4}=you\ can\ calculate$$

anonymous · Answer

.1296? and would I only use that formula for this type of question?

anonymous · Answer

and how come the .4 isn't used?

kropot72 · Answer

Your answer is correct. The probability distribution for the various possible numbers of successes, 0 to n, in n Bernoulli trials is the binomial distribution.
$$\left(\begin{matrix}n \ r\end{matrix}\right)p ^{r}q ^{n-r}$$
Applying the formula to your question:
$$\left(\begin{matrix}4 \ 0\end{matrix}\right)0.4^{0}0.6^{4}=(0.6)^{4}$$

anonymous · Answer

oh okay, so that formula just deals with numbers of success?

kropot72 · Answer

The formula deals with the probability of r successes and n - r failures.

anonymous · Answer

okay, thank you so much!

kropot72 · Answer

You're welcome :)