Question

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?

Answer 1

Answer:

0.17

Step-by-step explanation:

The number of times there is free Breakfast at work = 25%

The number of times the coworker lies = 1/3

The number of times the coworker speaks truth = 2/3

How likely is it that there is free breakfast at work today:

For this to happen both conditions must be satisfied. There must be free breakfast at work AND the coworker has also spoken truth. Now in this condition we will use the AND rule of Probability where we will take the Product of both the probabilities.

Result = 0.25 x 0.67 = 0.17

Answer 2

Answer:

$\frac{1}{6}$

Step-by-step explanation:

Data provided in the question:

Probability of free breakfast = 25% = 0.25

P( coworker lies | free breakfast ) = $\frac{1}{3}$

Therefore,

P(Coworker did not lie | Free Breakfast)

= 1 -  P( coworker lies | free breakfast )

= 1 -  $\frac{1}{3}$

=  $\frac{2}{3}$

Now,

P(Free breakfast at work | coworker told there is free breakfast)

=  P(Coworker did not lie | Free Breakfast) × P(Free breakfast)

= $\frac{2}{3}$ × 0.25

= $\frac{1}{6}$