answer all the following questions i bob has recently found four strange dice whose sides look a

I. (a) P(A>B) can be calculated by finding the probability of A having a 4 and B having a 3. Sin

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I. Bob has recently found four strange dice, whose sides look as follows: A: 4; 4; 4; 4; 0; 0 B: 3; 3; 3; 3; 3; 3 C: 6; 6; 2; 2; 2; 2 D: 5; 5; 5; 1; 1; 1 The 6 sides on each die are equally likely. Bob rolls each dice once. Let A be the result for die A, B be the result for die B, etc. (a) Find P(A>B); (b) Find P(B>C); (c) Find P(C>D); (d) Find P(D>A). (e) Is the event A > B independent of the event B > C? Explain your answer. II. Soton Bridge Club has 10 members. (a) In how many ways a president, vice president and treasurer can be chosen among the 10 members? (b) In how many ways three officers without predetermined titles can be chosen among the 10 members? [State clearly the formula you use to answer these two questions.] III. Assume that the probability that a lottery ticket is a winning ticket is p and this probability is independent of other tickets. Mary buys 3 tickets, hoping this will triple her chance of winning the lottery. (a) Write the formula of the Binomial Distribution that can be used to compute the probability that k of the 3 tickets are winning tickets? (b) What is the probability that none of the three tickets will win? (c) What is the probability that at least 1 of the 3 tickets will win?

          I. Bob has recently found four strange dice, whose sides look as follows:
A: 4; 4; 4; 4; 0; 0
B: 3; 3; 3; 3; 3; 3
C: 6; 6; 2; 2; 2; 2
D: 5; 5; 5; 1; 1; 1
The 6 sides on each die are equally likely. Bob rolls each dice once. Let A be the result for die A, B be the result for die B, etc.
(a) Find P(A>B);
(b) Find P(B>C);
(c) Find P(C>D);
(d) Find P(D>A).
(e) Is the event A > B independent of the event B > C? Explain your answer.

II. Soton Bridge Club has 10 members.
(a) In how many ways a president, vice president and treasurer can be chosen among the 10 members?
(b) In how many ways three officers without predetermined titles can be chosen among the 10 members?
[State clearly the formula you use to answer these two questions.]

III. Assume that the probability that a lottery ticket is a winning ticket is p and this probability is independent of other tickets. Mary buys 3 tickets, hoping this will triple her chance of winning the lottery.

(a) Write the formula of the Binomial Distribution that can be used to compute the probability that k of the 3 tickets are winning tickets?
(b) What is the probability that none of the three tickets will win?
(c) What is the probability that at least 1 of the 3 tickets will win?

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