Probability of Winning Lotto: Calculating E6, E5, En

[sara_87]

In ‘Lotto’ (a National Lottery game) there are 49 balls, each having a distinct number from the set
S = {1, 2, . . . , 49}. A draw consists of randomly choosing six ‘main’ balls followed by one ‘bonus’
ball. To play the game you choose six distinct numbers from S before the draw, and you win a
prize if any of the following events occur. Calculate the probability of each.
(a) E6: your choice matches all six main numbers;
(b) E5 : your choice matches any five main numbers plus the bonus ball;
(c) En: your choice matches any n main numbers, for n = 5, 4 and 3;

for part (a), i know the sample space is '49 choose 6' but what is the event space?
and i don't know how to do the other two, can someone help please?
thank you

 

[mgb_phys]

See discussion here http://plus.maths.org/issue29/features/haigh/index.html

 

[sara_87]

it's very interesting...i like it but i still can't figure out how to do it

 

[EnumaElish]

For (a), think of the simple experiment where two coins are flipped. What is the probability that they match? Next, think of the experiment where two dice are rolled. What is the probability that they match?

What is the common principle in these two experiments?

Suppose the 6 main balls have been drawn. You know this, but do not know their values. What is the probability that 6 particular balls have been drawn? Let that probability be p. What is the probability that you will make the same draw? What is the probability that both the lottery assistant and you will make this same draw?