1) A state lottery game requires that you pick 6 numbers correctly from 1 to 99.

Question

1) A state lottery game requires that you pick 6 numbers correctly from 1 to 99.
(a) How many ways are there to choose 6 numbers if order is not important?
(b) How many ways are there to choose 6 numbers if order matter?
(c) Assuming order is unimportant, what is the probability of picking all 6 numbers correctly?

2) A recent study found that 85% of breast-cancer cases are detectable by mam- mogram. Suppose a random sample of 15 women with breast cancer are given mammogram. find the probability of the following
(a) All of the cases are detectable
(b) None of the cases are detectable
(c) Not all of the cases are detectable
(d) More than half the cases are detectable

THANK YOU AHEAD OF TIME!

Explanation / Answer

a) total numbers are 1 to 99 = 99 numbers

we have to choose 6

total ways = 99C6 = 1120529256

b) if order matter then we can change the rearrangement of the numbers choosen..

which will be 6!*1120529256 = 806781064320

c) there can only be 1 correct answer which matches the number

and total number which can be choosen will be 1120529256

probability = 1/1120529256 = 0.0000001

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