Answer:
The probability that a randomly selected person who preferred picnic responded by email is 0.3333.
Step-by-step explanation:
Let A = a person responded by phone, B = a person responded by email and X = a person prefers picnic.
Given:
![n(B)=2\times n(A)\\N=n(A)+n(B)\\=n(A)+2n(A)\\=3n(A)](https://tex.z-dn.net/?f=n%28B%29%3D2%5Ctimes%20n%28A%29%5C%5CN%3Dn%28A%29%2Bn%28B%29%5C%5C%3Dn%28A%29%2B2n%28A%29%5C%5C%3D3n%28A%29)
![P(X|A)= 0.20\\P(X|B)=0.05](https://tex.z-dn.net/?f=P%28X%7CA%29%3D%200.20%5C%5CP%28X%7CB%29%3D0.05)
The probability that a response was through email is:
![P(B)=\frac{n(B)}{n(A)}\\=\frac{2n(A)}{3n(A)}\\= \frac{2}{3}](https://tex.z-dn.net/?f=P%28B%29%3D%5Cfrac%7Bn%28B%29%7D%7Bn%28A%29%7D%5C%5C%3D%5Cfrac%7B2n%28A%29%7D%7B3n%28A%29%7D%5C%5C%3D%20%20%5Cfrac%7B2%7D%7B3%7D)
Then the probability that a response was through phone is:
![P(A)=1-P(A)\\=1-\frac{2}{3}\\ =\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%29%3D1-P%28A%29%5C%5C%3D1-%5Cfrac%7B2%7D%7B3%7D%5C%5C%20%3D%5Cfrac%7B1%7D%7B3%7D)
Compute the probability that a person prefers picnic:
![P(X)=P(X|A)P(A) +P(X|B)P(B)\\=(0.20\times\frac{1}{3})+(0.05\times\frac{2}{3})\\=0.10](https://tex.z-dn.net/?f=P%28X%29%3DP%28X%7CA%29P%28A%29%20%2BP%28X%7CB%29P%28B%29%5C%5C%3D%280.20%5Ctimes%5Cfrac%7B1%7D%7B3%7D%29%2B%280.05%5Ctimes%5Cfrac%7B2%7D%7B3%7D%29%5C%5C%3D0.10)
Determine the probability that a randomly selected person who preferred picnic responded by email using the conditional probability as follows:
![P(B|X)=\frac{P(X|B)P(B)}{P(X)}\\= \frac{0.05\times\frac{2}{3} }{0.10}\\=0.3333](https://tex.z-dn.net/?f=P%28B%7CX%29%3D%5Cfrac%7BP%28X%7CB%29P%28B%29%7D%7BP%28X%29%7D%5C%5C%3D%20%5Cfrac%7B0.05%5Ctimes%5Cfrac%7B2%7D%7B3%7D%20%7D%7B0.10%7D%5C%5C%3D0.3333)
Thus, the probability that a person who prefers picnic responded by email is 0.3333.
Answer:
2 + x
2 + (x)
x + (2)
Step-by-step explanation:
Switch them around.
<span>In other words how can I decrease or increase a percentage using one step</span>