Question

Every day, Kaori flips a fair coin. She practices her violin if and only if the coin comes up heads. Find the probability that she practices at least five days this week.

Answer 1

Answer:

$P(X\geq 5)=0.2266$

Step-by-step explanation:

-We know that this is a binomial probability distribution with p=0.5 and n=7, since a week has 7 days.

-The probability of practicing at least 5 days is :

$P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X\geq 5)=P(X=5)+P(X=6)+P(X=7)\\\\\\={7\choose 5}(0.5^5)(0.5^2)+{7\choose 6}(0.5^6)(0.5^1)+{7\choose 7}(0.5^7)(0.5^0)\\\\=0.1641+0.0547+0.0078\\\\=0.2266$

Hence, the probability of practicing at least 5 days is 0.2266