The amount of time it takes Alice to make dinner is continuous and uniformly distributed between 19 minutes and 45 minutes. What is the probability that it takes Alice more than 40 minutes to finish making dinner given that it has already taken her more than 35 minutes in the making of her dinner?

The probability is 0.5

Step-by-step explanation:

If the time follows a continuous and uniform distribution, the probability that Alice makes the dinner in less than x minutes is equal to:

where a and b are equal to 19 and 45 minutes respectively. So:

Now, Let's call A the event that Alice takes more than 40 minutes to finish making dinner and B the event that Alice takes more than 35 minutes to finish making dinner. So, the probability that it takes Alice more than 40 minutes to finish making dinner given that it has already taken her more than 35 minutes in the making of her dinner is equal to:

P(A/B)=P(A∩B)/P(B)

Then, the probability P(B) that Alice takes more than 35 minutes to finish is calculated as:

At the same way, the probability P(A∩B) that Alice takes more than 40 minutes to finish making dinner and Alice takes more than 35 minutes to finish making dinner is equal to the probability P(A) that Alice takes more that 40 minutes to finish making dinner, so it is calculated as:

Finally, P(A/B) is equal to:

26

step-by-step explanation: