Respuesta :
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
Data provided in the question:
Probability of free breakfast = 25% = 0.25
P( coworker lies | free breakfast ) = [tex]\frac{1}{3}[/tex]
Therefore,
P(Coworker did not lie | Free Breakfast)
= 1 - P( coworker lies | free breakfast )
= 1 - [tex]\frac{1}{3}[/tex]
= [tex]\frac{2}{3}[/tex]
Now,
P(Free breakfast at work | coworker told there is free breakfast)
= P(Coworker did not lie | Free Breakfast) × P(Free breakfast)
= [tex]\frac{2}{3}[/tex] × 0.25
= [tex]\frac{1}{6}[/tex]
The likelihood that there is free breakfast at work today is from the given scenarios is; 40%
How to solve probability?
Let X be the chance that both there is breakfast and your friend tells you there is breakfast.
Let Y be the chance that your friend tells you there is breakfast on any given day.
We are told that on any given day, there is 1/4 chance of breakfast and 2/3 chance of your friend telling the truth.
There are are a total of 12 possibities but the breakdown of the likely ones are;
- Breakfast (2/3 times, he will tell you there is Breakfast and there is)
- No Breakfast (1/3 times, he will tell you there is Breakfast and there is not)
- No Breakfast (1/3 times, he will tell you there is Breakfast and there is not)
- No Breakfast (1/3 times, he will tell you there is Breakfast and there is not)
We can say that there is a 5/12 chance that, on any given day, your friend will tell you there is breakfast. Thus; Y = 5/12
Amongst the 12 possible scenarios we see that there was both Breakfast plus your friend telling you there is breakfast twice. Thus;
X = 2/12
Thus;
The likelihood that there is free breakfast at work today is;
X/Y = (2/12)/(5/12) = 2/5 = 40%
Read more about probability at; https://brainly.com/question/25870256
