25% of the time there is free breakfast at work. You just woke up and are really hungry, so you call your coworker who is already at work, and he tells you there is free breakfast. However, he lies to you 1/3 of the time. How likely is it that there is free breakfast at work today? *
Answers
Answer:
Chances that there is free breakfast at work is 1/6
Step-by-step explanation:
The probability that there is free breakfast at work is given by:
P(breakfast at work) = 25/100 = 1/4
Now, if your friend lies to you 1/3 of the time, there's 1/3 possibility that the breakfast may not be there.
So, the probability that your friend is telling the truth is = 1 - 1/3 = 2/3
The probability that there is free breakfast and that your friend is telling the truth is:
= P(Free Breakfast and Friend telling the truth) = 1/4 × 2/3 = 2/12 = 1/6
It is 1/6 likely that there is free breakfast at work.
Answer:
2/5 (or 40%)
Step-by-step explanation:
We need to determine the chance that, on a day where your friend tells you there is breakfast, there is actually breakfast.
To solve for this, we need to divide X (the chance that both there is breakfast and your friend tells you there is breakfast) by Y (the chance that your friend tells you there is breakfast on any given day).
Let's solve for Y, first.
On any given day, there is 1/4 chance of breakfast and 2/3 chance of your friend telling the truth. The 12 possible breakdowns therefore are as follows:
-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)
Thus, there is a 5/12 chance that, on any given day, your friend will tell you there is breakfast. Y = 5/12
Let's now solve for X.
What are the chances that your friend tells you there is breakfast AND there is actually breakfast?
Of the 12 possible scenarios (described when solving for Y, above) there was both Breakfast + your friend telling you there is breakfast TWO times.
Thus, 2/12 = X
Now, let's solve the problem:
X/Y = (2/12) / (5/12) = 2/5 (or 40%)