Question

Let event A=It rains on Thursday. Which event is most likely to be independent of A? a. it rains on friday b. it is cloudy on thursday c. you have milk with breakfast on wednesday d. a customer buys an umbrella on thursday

Answer 1

The event that is most likely to be independent of event A is that it is cloudy on Thursday.

Step-by-step explanation:

The question is asking which event is most likely to be independent of event A, which is defined as 'It rains on Thursday'.

To determine independence, we need to consider if the occurrence of event A affects the probability of the other events happening. If the probability of event B remains the same whether event A occurs or not, then event B is independent of event A.

Among the given options, the event that is most likely to be independent of event A is b. It is cloudy on Thursday. The occurrence of rain on Thursday does not affect the probability of it being cloudy on Thursday. The weather conditions each day are independent of one another.

Answer 2

Option (c) "You have milk with breakfast on Wednesday" are most likely to be independent of event A.

Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other. Let's analyze each option in relation to event A (It rains on Thursday):

a. It rains on Friday:

While not directly dependent on Thursday's rain, weather patterns can sometimes influence consecutive days. So, there might be a slight correlation, making it less likely to be independent than option b.

b. It is cloudy on Thursday:

Cloudiness and rainfall can be related, so the occurrence of rain on Thursday might influence the probability of cloudiness. These events may not be entirely independent.

c. You have milk with breakfast on Wednesday:

The choice of having milk with breakfast on Wednesday is likely to be independent of whether it rains on Thursday. These events are unrelated.

d. A customer buys an umbrella on Thursday:

The probability of a customer buying an umbrella on Thursday might be influenced by whether it rains on Thursday. These events may not be entirely independent.

So, the answer is: c. you have milk with breakfast on Wednesday

This is based on the assumption that the choice of having milk with breakfast on Wednesday is unrelated to Thursday's rainfall.

Question:

Let event A=It rains on Thursday. Which event is most likely to be independent of A?

a. it rains on Friday

b. it is cloudy on Thursday

c. you have milk with breakfast on Wednesday

d. a customer buys an umbrella on Thursday