Question

Assume that a procedure yields a binomial distribution with a trial repeated n = 9 times. Find the probability of x = 4 successes given the probability p = 0.59 of success on a single trial. (Report answer accurate to 4 decimal places.) P ( 4 ) =

Answer 1

We have a closed formula to get the probability of having a certain number of successes over repeated trials following a binomial distribution.

The formula is

`\displaystyle P(X=k)=\binom{n}{k}p^k(1-p)^(n-k)`

Where:

• 
  `X` is the random variable
• 
  `n` is the number of trials
• 
  `k` is the number of desired successes
• 
  `p` is the probability of success

So, in your case, the probability becomes

`\displaystyle P(X=4)=\binom{9}{4}0.59^4(0.41)^(5)\approx 0.1768`