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# S2 probability question (how do i do it?) watch

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1. 4 (a) State clearly the conditions under which it is appropriate to assume that a random variable has a binomial distribution
(1) fixed number of trials, (2) each trial is either a success or failure, (3) the probability of a success/failure is constant, (4) the events are independent

A door-to-door canvasser tries to persuade people to have a certain type of double glazing installed. The probability that his canvassing at a house is successful is 0.05

(b) Find the probability that he wll have at least 2 successes out of the first 10 houses he canvasses

P(X>=2) = 1 - P(X=<2), then work out from cumulative binomial table (is this right?)

(c) Find the number of houses he should canvass per day in order to average 3 successes per day.

how do i do this part? :O any help would be much appreciated, thanks
2. For (b) that's not right. Since you're using discrete data, you can use either or .

For (c), you need to think about the expectation. That is, you need to find the number of houses for which .
3. (Original post by nuodai)
For (b) that's not right. Since you're using discrete data, you can use either or .

For (c), you need to think about the expectation. That is, you need to find the number of houses for which .
ah yeah i see what you mean about (b)

and for (c), expectation = np right? so 3 = 0.05n, n = 3/0.05. is this the correct answer then?

p.s. part (d) says: Calculte the least number of houses that he must canvass in order that the probability of him getting at least one success exceeds 0.99

i don't understand this at all, care to push me in the right direction? would be much appreciated
4. (Original post by doin' your mum)
ah yeah i see what you mean about (b)

and for (c), expectation = np right? so 3 = 0.05n, n = 3/0.05. is this the correct answer then?
Yup.

(Original post by doin' your mum)
p.s. part (d) says: Calculte the least number of houses that he must canvass in order that the probability of him getting at least one success exceeds 0.99

i don't understand this at all, care to push me in the right direction? would be much appreciated
This is finding the range of values of such that , and then the answer is the smallest value of in this range. Using the right formula in the inequality and rearranging will give you an answer in the form -- bear in mind that if you have say (picked at random, not actually the answer) then the answer would be 33.

The hardest part in most S2 problems is converting the word problem into a mathematical formula for you to solve... once you've got that down you'll be able to do these without any problems. Can you see where I got from?

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