P(X) X 1 0.125 2 0.125 1 0.125 3 0.125 1 0.125 2 0.125 4 0.125 0.125 Frequency of spins Frequency 200 150 100 50 10 12 Spaces st

Consider the situation that two events A and B are independent. P(A) = 0.2 and P(B)= 0.5. What is the probability that both events A and B occur?

The probability of afternoon rain given morning cloud cover >50% is of interest to those forecasting the weather. You can calculate this probability using Bayes' Theorem (below). The probability of morning cloud cover in general is 30% in the area you are concerned with and when there's afternoon rain, morning cloud cover of the kind described above occurs 90% of the time. The probability of rain in general for the area is about 26% of days. From the above information, identify what P(BIA) would be. Express your answer as a proportion, rounded to two decimal places. P(A/B)= = P(B|A)*P(A) P(B)

QUESTION 2 a) Based on the past data, 8% of customers will order a dessert with the meal at a noodle's restaurant. 14% of them will order a bottled beverage. i. What is the probability that a customer will order both a dessert and a bottled average? (2 marks) ii. The customers have ordered a dessert with the meal. Calculate the probability that he or she will order a bottled beverage. (2 marks) b) The Graduate Management Admission Test (GMAT) is a requirement for all applicants of MBA programs. A variety of preparatory courses are designed to help applicants improve their GMAT scores, which range from 200 to 800. Suppose that a survey of MBA students reveals that among GMAT scorers at least 650, 72% took a preparatory course; whereas among GMAT scores of less than 650 only 31% took a preparatory course. The probability for an applicant to score at least 650 is 30%. Suppose he was not taking the preparatory course. What is his probability of achieving 650 or more for GMAT score? (5…