Answer:
The probability of selling more than 2 properties in one week=0.9453
Step-by-step explanation:
We are given that
n=10
p=50%=0.50
q=1-p=1-0.50=0.50
We have to find the probability of selling more than 2 properties in one week.
Binomial probability distribution formula
[tex]P(X=x)=nC_xp^{x}q^{n-x}[/tex]
Using the formula
[tex]P(x\geq 2)=10C_0(0.50)^{10}+10C_1(0.50)^{10}+10C_2(0.50)^{2}[/tex]
[tex]P(x\leq 2)=\frac{10!}{0!10!}(0.50)^{10}+\frac{10\times 9!}{9!}(0.50)^{10}+\frac{10\times 9\times 8!}{2\times 1\times 8!}(0.50)^{10}[/tex]
Using the formula
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]
[tex]P(x\leq 2)=(0.50)^{10}+10(0.50)^{10}+45(0.50)^{10}[/tex]
[tex]P(x\leq 2)=(0.50)^{10}(1+10+45)[/tex]
[tex]P(x\leq 2)=56(0.50)^{10}[/tex]
Now,
[tex]P(x>2)=1-P(x\leq 2)[/tex]
[tex]P(x>2)=1-56(0.50)^{10}[/tex]
[tex]P(x>2)=0.9453[/tex]
Hence, the probability of selling more than 2 properties in one week=0.9453
