solve the following questions ( handwritten) solution only neatly and clean it must be complete read instructions.

Subj: Math

. Determine the following probabilities. a. The probability of drawing first a diamond then a spade in 2 successive draws from a deck of 52 playing cards. (2 pts) b. The probability of drawing one heart and a spade in 2 successive draws of cards from a deck of 52 playing cards. (2 pts) c. The probability of drawing a king or queen or an ace in one single draw of a card from a deck of 52 well shuffled cards. (2 pts) . If P(A) = 1/3 and P(B) = 1/6 and A and B are mutually exclusive events, what is P(A and B)? (2 pts) . Suppose P(A) = 0.25 and P(B) = 0.15. If A and B are independent events but not mutually exclusive, find P(A and B). (2 pts) . In a field of 10 racecars, in how many different ways could they place first, second and third in a race? (2 pts) . There are 20 members of the group aCAPela, a group of talented singers from CAP College. Of the 20 members, six are males. In joining a local talent contest, aCAPela has to field only 6 members. What is the probability that a. All six will be males? (2 pts) b. All six will be females? (2 pts) c. First 3 will be females and the remaining slots are males? (2 pts) 6. Determine the value of n from: nP3 =5 (4P) (2 pts) 7. Consider the experiment of throwing two coins, a. establish the probability distribution (2 pts) b. determine the expected value (2 pts) c. determine the standard deviation (2 pts) . The average weight of the incoming freshmen of the PMA is 150 Ibs. with a standard deviation of 15 Ibs. (Assume normal distribution for the weight). a. What is the probability of the incoming freshmen weighing between 125 and 175 Ibs.? (2 pts) b. What is the minimum weight of the heftiest 10% of the incoming freshmen? (2 pts) 1. Discuss the types of Sampling Distribution based on your understanding. (3 pts for each Sampling Distribution) 2. A simple random sample of 30 people from a certain class has a mean weight of 133 Ibs. Can we conclude that the mean weight of the class is not 125 lbs? The standard deviation is known to be 40. Assume a significance of 0.10. (10 pts) 3. Test the independence of each sport based on the number of active league for each of the region. Assume a significance of 0.05 (10 pts) Region 1 Region 2 Region 3 Basketball 75 58 48 Soccer 33 15 23 Volleyball 47 36 29 4. Given the following Data: Player Age Points Per Game Bosh 29 15.1 Bryant 36 26.7 Durant 25 28.9 James 29 23.4 Nowitzki 35 19.9 Rose 23 27.6 Wade 32 20.9 a. Find the Correlation Coefficient. (5 pts) b. Determine a, b and the equation of the line that best fits the given set of data. (10 pts)