Answer :
Answer:
The probability that exactly 2 don't grow is 0.075 or 7.5%
Step-by-step explanation:
Binomial Distribution
Let's consider a random experience with only two possible outcomes. Call p to the probability that the event has a successful outcome and q to the unsuccessful outcome.
It's clear 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 following formula:
[tex]\displaystyle P_{x} = {n \choose x} p^{x} q^{n-x}[/tex]
Where
[tex]\displaystyle {n \choose x}[/tex]
Is the number of combinations:
[tex]\displaystyle {n \choose x} =_nC_x=\frac{n !}{x ! (n-x) !}[/tex]
For the problem to solve, each seed has a p=0.95 probability of growing into a healthy plant. The value of q=1-0.95=0.05.
The experience is repeated n=10 times and we want to estimate the probability that 2 of them don't grow. Note this last data is not directly the value of x because it's not related to success but with no success. The value of x is x=10-2=8. That means, 8 out of 10 seeds grow.
Apply the formula:
[tex]\displaystyle P_{8} = {10 \choose 8} \cdot 0.95^{8} \cdot 0.05^{10-8}[/tex]
[tex]\displaystyle P_{8} = 45\cdot 0.95^{8} 0.05^{2}[/tex]
[tex]\displaystyle P_{8} = 0.075[/tex]
The probability that exactly 2 don't grow is 0.075 or 7.5%