Answer:
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:
[tex]\displaystyle P_{x} = {n \choose x}\cdot p^{x}\cdot q^{n-x}[/tex]
Where :
[tex]\displaystyle {n \choose x}[/tex]
Is the number of combinations, calcula ted as follows:
[tex]\displaystyle {n \choose x} =_nC_x=\frac{n !}{x ! (n-x) !}[/tex]
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:
[tex]\displaystyle P_{4} = {8 \choose 4}\cdot 0.7^{4}\cdot 0.3^{8-4}[/tex]
[tex]\displaystyle P_{4} = 70\cdot 0.7^{4}\cdot 0.3^{4}[/tex]
[tex]\displaystyle P_{4} = 0.1361[/tex]
Thus, the probability that exactly 4 don't grow is 0.1361 or 13.61%
