If a seed is planted, it has a 70% chance of growing into a healthy plant. If 8 seeds are planted, what is the probability that exactly 4 don't grow?

Thus, the probability that exactly 4 don't grow is 0.1361 or 13.61%

Step-by-step explanation:

Binomial Distribution

Consider a random experience that has only two possible outcomes: Success or Failure. Let's call p to the probability that the event has a successful outcome and q to the failure outcome.

It follows that p+q=1, or q=1-p.

Now repeat the random experience n times. We want to calculate the probability of getting x successful outcomes. This can be done with the Binomial Distribution formula:

Where :

Is the number of combinations, calcula ted as follows:

A planted seed has a 70% chance of growing into a healthy plant. The successful outcome has p=0.7 and q=0.3.

The experience is repeated n=8 times. We want to calculate the probability of having 4 failures (not growing seeds) or x=4 successes.

Apply the formula:

Thus, the probability that exactly 4 don't grow is 0.1361 or 13.61%

-4

step-by-step explanation: