# Thread: Probability revision question

1. ## Probability revision question

Hi there id be thankful for any help anyone out there can give me with this revision question

Q) Anne takes part in a quiz. She has to answer 10 questions. She scores 3 points if she can answer a question correctly by herself. If she cannot answer a question correctly she text messages a friend who may be able to give her the correct answer. If she obtains a correct answer in this fashion she scores 2 points. If not, she loses a point. she estimates that the probability of answering any question correctly by herself is 0.7 and the probability of her friend supplying a correct answer is 0.8

i) what is the probability of Anne answering any given question correctly?

ii) What is the average number of points that Anne will score if she answers 10 questions?

i get 0.94 for part i) can anyone help me out with part ii)?

Cheers........... :-)

2. Hello,

part ii) will be the expected value, defined this way :

$\displaystyle E(X)=\sum_{x \in \chi} x P(X=x)$

Here, the possible values for X are 3, 2 or -1 (if she finds the correct answer on her own, or thanks to her friend, or mistake).

So $\displaystyle E(X)=3*P(X=3)+2*P(X=2)-1*P(X=-1)$

P(X=3) : probability that she's right
P(X=2) : probability that she got wrong, then that her friend got right
P(X=-1) : probability that she's wrong and that her friend too

3. ## part ii) amended

Thanx Moo, i typed part ii) wrongly the first time it should be as follows

Part ii) What is the average number of points (to the nearest whole number) that Anne will score if she answers 10 questions

I have the answer sheet and the answer is given as 25, but i cant work this out for myself, could you help me out some more please.

Cheers

4. Then, multiply it by 10

P(X=3) : probab that she answers correctly on her own -> 0.7
P(X=2) : she answers wrong but her friend answers correctly -> 0.3*0.8=0.24
P(X=-1) : she answers wrong and so does her friend -> 0.3*0.2=0.06

The average is : 10(3*P(X=3)+2*P(X=2)-P(X=-1))

And I get something round the answer, but I didn't use any calculator, so do it on your own