Probability

Can someone help me with 6b please I don’t understand why my method is wrong.

https://imgur.com/a/aC1v2E4

Can someone help me with 6b please I don’t understand why my method is wrong.

https://imgur.com/a/aC1v2E4

0.43 is the probability his phone fails at least once, in a given week.

So for it to fail in three weeks in a row, it's just 0.43^3.

Not sure exactly what you're doing, but his phone fails at least once a week? So I would do something like
1 - p(fail only once)^3

Yeah that’s what they wrote. But what does the second part mean because I think that’s what I was trying to do.

I made that mistake too. But it doesn’t want 3 consecutive fails

Eh, that wording could be clearer.

In which case, here's the breakdown of what they mean:

We can either have the phone failing 3 weeks in a row, at least once every week, which is the probability 0.43^3.

But we can also have the phone failing in two weeks, while in one of those week's it's OK. The probability of this happening is (0.43^2)*(0.57). But this can occur in exactly (3 choose 2) number of ways; say, (Fail,Fail, OK) or (Fail, OK, Fail) or (OK, Fail, Fail)

and similarly with the case where we can have 1 week it fails more once once, and the other two weeks are OK.


Adding them up agrees with the answer.