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AS paper Binomial distribution and probability

Struggling most with part iii)...

The probability that Janice sees a kingfisher on any particular day is 0.3. She notes the number, X, of days in a week on which she sees a kingfisher.

(i) State one necessary condition for X to have a binomial distribution. [1]

Assume now that X has a binomial distribution.

(ii) Find the probability that, in a week, Janice sees a kingfisher on exactly 2 days. [1]

Each week Janice notes the number of days on which she sees a kingfisher.

(iii) Find the probability that Janice sees a kingfisher on exactly 2 days in a week during at least 4 of 6 randomly chosen weeks.

Thanks in advance :smile:
If you define Y to be the number of weeks (out of 6) in which Janice sees a kingfisher on exactly 2 days (in that week), then Y will be binomially distributed with p the value you calculated in (ii).
Reply 2
Avatar for scarlettih
scarlettih
OP
12
Original post by DFranklin
If you define Y to be the number of weeks (out of 6) in which Janice sees a kingfisher on exactly 2 days (in that week), then Y will be binomially distributed with p the value you calculated in (ii).

Thanks so much, sorry got a bit mixed up... I'm stuck on ii too.
Original post by scarlettih
Struggling most with part iii)...

The probability that Janice sees a kingfisher on any particular day is 0.3. She notes the number, X, of days in a week on which she sees a kingfisher.

(i) State one necessary condition for X to have a binomial distribution. [1]

Assume now that X has a binomial distribution.

(ii) Find the probability that, in a week, Janice sees a kingfisher on exactly 2 days. [1]

Each week Janice notes the number of days on which she sees a kingfisher.

(iii) Find the probability that Janice sees a kingfisher on exactly 2 days in a week during at least 4 of 6 randomly chosen weeks.

Thanks in advance :smile:


You found the probability that she sees kingfisher exactly 2 days on any given week. Lets label this as our probability p.

Now consider the having 6 weeks. On each week, she has a probability p of seeing kingfisher twice. This can be modelled once more using binomial distribution Y~B(6,p) where Y is the number of weeks she sees kigfisher exactly twice.

You seek P(Y≥4)P(Y \geq 4)
Original post by scarlettih
Thanks so much, sorry got a bit mixed up... I'm stuck on ii too.

Not to be mean, but if you can't do (ii), then it would seem you don't know anything about binomial distributions at all. This forum is good for helping people who know the material over little humps and problems, but if you haven't covered the subject at all, you really need to do that first.
Reply 5
Avatar for scarlettih
scarlettih
OP
12
Original post by DFranklin
Not to be mean, but if you can't do (ii), then it would seem you don't know anything about binomial distributions at all. This forum is good for helping people who know the material over little humps and problems, but if you haven't covered the subject at all, you really need to do that first.

No worries got it now! Just needed my memory jogging. Thanks for being honest ahah I haven't covered it in a long time...

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