MAT 103A Assignment #3 (Probability theory) Q1. Two cards are drawn together from a pack of 52 cards. Draw a tree diagram and find the probability that one card is a spade and one is a heart. Q.2. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag without replacement, draw a nice tree diagram and find the probability of getting at most a red ball. Tab ar Q3. Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Tom takes the test and scores 585. Will he be admitted to this university? Q4. The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. a) What percent of people earn less than $40,000? b) What percent of people earn between $45,000 and $65,000? c) What percent of people earn more than $70,000? Q1. Define A: {the wom B: {the won Q5. Two dice, one blue and one orange, are rolled simultaneously. Find the probability of getting (i) equal numbers on both (ii) two numbers appearing on them whose sum at least 9. C: (the woma