Q2 part a ab b 2 of 10 COMBINATORICS (A Take-Home Problem) 2. Megabucks is a lot

Question

Q2 part a ab b

2 of 10 COMBINATORICS (A Take-Home Problem) 2. Megabucks is a lottery game played in Massachusetts. A random drawing of 6 numbers out of all 36 numbers from 1 to 36 is made. In problems below you can give answers in terms of combinatorial symbols (combinations, permutations, etc.) (4 pts.) To win the jackpot should have correct all the 6 numbers drawn regardless of their order. (A filled ticket contains 6 numbers.) What is the probability that a randomly filled ticket wins the jackpot? a. (which is usually worth several million dollars) a ticket Answer: (7 pts.) A player who correctly chooses (exactly) five out of the six winning numbers gets $500. What is the probability of winning $500? b. Answer: Emai Sav ANALYSIS OF VENN DIAOKAIVI

Explanation / Answer

Solution

Back-up Theory

Number of ways of selecting r things out of n things is given by nCr = (n!)/{(r!)(n - r)!}……(1)

Probability of an event E, denoted by P(E) = n/N ……………………………………………(2)

where n = n(E) = Number of outcomes/cases/possibilities favourable to the event E and N = n(S) = Total number all possible outcomes/cases/possibilities.

Part (a)

6 out of 36 cards can be drawn in 36C6 ways…………………………………………………..(3)

Out of these many ways, only one selection will have all the six numbers tallying. Thus, probability of jackpot = 1/36C6 = 1/1947792 ANSWER

Part (b)

5 out of 6 cards can be tallying in 6C5 = 6 ways……………………………………………..(4)

(3), (4) and (2) =>

probability of winning $500 = 6/36C6 = 1/324632 ANSWER

DONE

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