# Question4/6+4-10 marks 6)Fill up with the probability of respective event in the probability tree diagram of...

###### Question:

Question4/6+4-10 marks 6)Fill up with the probability of respective event in the probability tree diagram of a family with three Children. Use B for boy and G for girl. 25 16 25 16 186 28 15 17 235 From the diagram find the probability that the family has (a) Three boys (b) More than two boys (c) At least one boy C) The medal distribution from the 2000 Summer Olympic Games is shown in the table Gold Silver Bronze United States Russia 3228 China Australia Others Choose one medal winner at random. (a) Find the probability that the winner won the gold medal, given that the winner was from the United States (b) Find the probability that the winner was from the United States, given that she or he won a gold medal Question5j5+5–10 marks A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain O no more than 2' rejects? at least "2" rejects? (ii) Mean and the variance of the distribution
(b)The following table provides a probability distribution for the random variable y. X P(x) 2 0.30 Recall; E(Ⓡ) === *P(x) 4 0.20 7 0.40 Var(x) = 0= (x – u)?p(x) 8 0.10 a. Is this probability distribution valid? Explain. b. What is the probability that x=7? c. Compute E(x). d. Compute the variance of Question6[4+3+3=10 marks (a) Upon a child's birth, a deposit is made into an account. Assume that the account has an annual interest rate of 4.8% compounded quarterly. How much must be deposited now so that the child will have $60,000 at age 18 (b) If$700 is borrowed and the interest after 18 months is $136.5, what is the annual interest rate for a simple interest loan? [Simple interest] (c) Example:$2,500 is needed in 2 years for a purchase. A bank offers a certificate of deposit (CD) that pays 4% annual interest computed using simple interest. How much must be put in this CD now to have the necessary money in 2 years?

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