Answer:
[tex]P(X\geq 5)=0.2266[/tex]
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 :
[tex]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[/tex]
Hence, the probability of practicing at least 5 days is 0.2266
The probability that she practices at least five days this week is P = 0.227
Kaori trains when she gets heads on the flip of a coin, and we know that this happens with a probability of 0.5,
Then the probability that she practices at least 5 times this week, is equal to the probability of getting heads 5 times, plus the probability of getting heads 6 times, plus the probability of getting heads 7 times.
The probability of getting heads x out of 7 times is:
P(x) = (0.5)^7*C(x, 7)
Where:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
Then we will have:
[tex]P = P(5) + P(6) + P(7)\\\\P = (0.5)^7*(C(7, 5) + C(7, 6) + C(7,7))\\\\P = (0.5)^7*( \frac{7!}{5!*2!} + \frac{7!}{6!*1!} + \frac{7!}{7!} )\\\\P = (0.5)^7*( 7*3 + 7 + 1) = 0.227[/tex]
The probability that she practices at least five days this week is P = 0.227
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
