> dpois(3,0.1224) [1] 0.0002704179 > ppois(3,0.1224) [1] 0.9999915 > dbinom(3,6,
ID: 3049501 • Letter: #
Question
> dpois(3,0.1224)
[1] 0.0002704179
> ppois(3,0.1224)
[1] 0.9999915
> dbinom(3,6,0.1224)
[1] 0.02478929
> pbinom(3,6,0.1224)
[1] 0.9972589
> dhyper(3,6,43,6)
[1] 0.0176504
> phyper(3,6,43,6)
[1] 0.9990129
> dnbinom(3,6,0.1224)
[1] 0.0001272818
> pnbinom(3,6,0.1224)
[1] 0.0002027389
You play Lotto 6-49 by choosing 6 different numbers between 1 and 49. Then
6 different winning numbers are randomly drawn. We are interested in the
number of your numbers that match the winning numbers.
a. (4 marks) What probability distribution may be an appropriate model in
this situation? Justify your choice and report its parameters.
b. (2 marks) What is the probability that you'll win a share of the bigger
prizes? This happens if you match more than 3 numbers. Potentially
useful R output is included above.
Explanation / Answer
a)
as here sampling is done without replacement therefore numbers are depdent on prior choice Hence we should use hypergeometric distribution.
b) probability that you'll win a share of the bigger
prizes =1-P(matches at most 3 numbers)
=1-> phyper(3,6,43,6)
[1] 0.9990129 =1-0.9990129=0.0009871
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