Question

Every day, a lecture may be canceled due to inclement weather with probability 0.05. Class cancelations on different days are independent. (a) There are 15 classes left this semester. Compute the probability that at least 4 of them get canceled. (b) Compute the probability that the tenth class

Answer 1

(a)Probability of cancelling at least 4 classes  is 0.0055.

(b)Probability of 10th class is third class that gets cancelled  = 0.0031

Step-by-step explanation:

Here, the question is incomplete.

Every day, a lecture may be canceled due to inclement weather with probability 0.05. Class cancellations on different days are independent.

(a) There are 15 classes left this semester. Compute the probability that at least 4 of them get canceled.

(b) Compute the probability that the tenth class this semester is the third class that gets canceled.

Now, here:

The probability of cancelling each class  = 0.05

Now, probability of cancelling at least 4 classes

= 1 - P(Cancelling  at max 3 classes)

=  1 - P(0 ≤ x  ≤  3)   = 1 - Binomial (15,0.05,3)

= 0.0055

Hence, probability of cancelling at least 4 classes  is 0.0055.

(b) As given, 10th class is third class that gets cancelled.

So, the first and second classes that get cancelled in between 1 - 9.

P(2 class cancelled in 1st 9) = Binomial (15,0.05,3) = 0.0629

Also, as given  P(10th class cancelled) = 0.05

⇒ P(10th class is third class that gets cancelled ) = 0.0629 x 0.05 = 0.0031