Answer :
Answer:
P(x=5)=0.2
Step-by-step explanation:
Binomial Distribution
Consider a random event that has 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 event 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]
Calculate the probability for n=10, p=0.4, x=5. It follows that q=1-p=0.6:
[tex]\displaystyle P_{5} = {10 \choose 5}\cdot 0.4^{5}\cdot 0.6^{10-5}[/tex]
[tex]\displaystyle P_{5} = 252\cdot 0.4^{5}\cdot 0.6^{5}[/tex]
[tex]P_{5} = 0.2[/tex]
P(x=5)=0.2