a) Ellisa is going to play one badminton match and one tennis match. The badminton match has been scheduled one week earlier than the tennis match. Based on the prediction by her coach, the chance...

Extracted text: a) Ellisa is going to play one badminton match and one tennis match. The badminton match has been scheduled one week earlier than the tennis match. Based on the prediction by her coach, the chance that she will win the badminton match is 0.9. Other than that, the coach believed that if Ellisa wins the badminton match, the chance that she will win the tennis match is 0.65. But if she loses the badminton match, she has a 0.7 chance of losing the tennis match too. i) Draw a tree diagram and the probabilities for each event involved in the above scenario. ii) Find the probability that Ellisa will win the tennis match. iii) Are the events independent? Proof it numerically. b) According to a survey conducted by Tourism Malaysia, 70% of Malaysian companies give employees 25 to 30 days of annual leave. Find the probability that among 6 companies surveyed at random, more than half of the companies give employees 25 to 30 days of annual leave. c) The time taken for servicing a car has an average time of 17 minutes and a standard deviation of 2.2 minutes. If the service times are approximately normally distributed, i. Find the probability that the time taken for servicing Ali's car is between 15 to 20 minutes. ii. What is the maximin service time for 90% of the cars?