Question

IT × |メStudent/Parent Dashboard x ? Exam 5 xA radio show host broadcasts t s//primaverahsstrongmind.com/courses/2724/assignments/490663?module item id-1341383 Rafaela is getting ready to take the bus to her job today. She checks the weather forecast and finds that there is a 50% chance for rain. Rafaela knows that when it rains, there is a 10% chance that her bus will be late to pick her up. on days that there is at least a 9% chance of her getting stuck in the rain wating for the bus Rafaela packs an umbrella. She decides to pack an umbrella today. Part A: Did Rafaela make a wise decision? Part B: While Rafaela is at work, the weather forecast changes to an 80% chance of rain in the afternooneeng What is the probability that Rafaela will need to use her umbrella while waiting for a late bus to take her home? Select one answer that is completely correct for Part A, and select one answer for Part B B: The updated weather forecast increases the probability of needing an umbrella to 9% A: Yes, Rafaela should have packed the umbrella. The probability of rain and the probability of a late bus are mutually inclusive events, and the probability of both occurring is 60%. B: The updated weather forecast increases the probablity of needing an umbrela to 16% A: Yes, Rafaela should have packed the umbrella. The probability of rain and the probability of a late bus are mutually exclusive events, and the probability of both occurring is 60%. A: No. Rafaela did not need to pack an umbrella. The probability of rain and the probability of a late bus are dependent events, and the probability of both occurring is only 5% B: The updated weather forecast incases the probabity or needing an umbrella to 90% A: No. Rafaela did not need to pack an umbrela. The probability of rain and the probablity of a late bus are independent events and the probabilty of botn occurring is ony 5%. B. The updated weather forecast increases the probab ity of needing an umbrela to 8%, search

Answer 1

Solution

Back-up Theory

If A and B are two events such that probability of B is influenced by occurrence or otherwise of A, then, Conditional Probability of B given A, denoted by P(B/A) = P(B ∩ A)/P(A)……....….(1)

Now to work out the solution,

Let A and B respectively represent the events that there is rain and the bus comes late.

Then, the given data would, in probability language, be:

P(A) = 0.5 and P(B/A) = 0.1

Part (a)

Probability of rain and bus coming late

= P(B ∩ A)

= P(B/A) x P(A) vide (1),

= 0.5 x 0.1

= 0.05, i.e., 5%

Since 5% is less than the stipulated 9%, there no need to pack the umbrella.

Thus Third Option of A Answer

Part (b)

Now, P(A) = 0.8 and hence P(B ∩ A) = 0.08 i.e., 8%

Thus Last Option of B. Answer

DONE