# Probability of the next event, given the previous one

• May 22nd 2011, 07:06 AM
Mcoolta
Probability of the next event, given the previous one
Past Paper exam Question which i need help on.

Two colours of sweets; Red and Green. The two types are mixed into bags by one of two mixing machines. Mixer A produces 40% red, and 60% green. Mixer B produces 70% red and 30% green. Mixer A is used 30% of the time.

(i) What is the probability the 1st sweet chosen is red?
(ii) If it is red, what is the probability the packet was mixed by machine A?
(iii) If the second sweet from the same packet is also red, what now is the probability the packet was mixed by machine A?

(i) So for this, ive got;

P(R) = P(R|A)P(A) + P(R|B)P(B)
P(R) = 0.4 x 0.3 + 0.7 x 0.7 = 0.61

(ii)

P(A|R) = [P(R|A)P(A)]/P(R)
P(A|R) = 0.12/0.61 = 12/61

Is this correct so far? How do i go about working out part (iii)?
• May 22nd 2011, 07:25 AM
Plato
Quote:

Originally Posted by Mcoolta
Two colours of sweets; Red and Green. The two types are mixed into bags by one of two mixing machines. Mixer A produces 40% red, and 60% green. Mixer B produces 70% red and 30% green. Mixer A is used 30% of the time.
(i) What is the probability the 1st sweet chosen is red?
(ii) If it is red, what is the probability the packet was mixed by machine A?
(iii) If the second sweet from the same packet is also red, what now is the probability the packet was mixed by machine A?
(i) So for this, ive got;
P(R) = P(R|A)P(A) + P(R|B)P(B)
P(R) = 0.4 x 0.3 + 0.7 x 0.7 = 0.61

(ii) P(A|R) = [P(R|A)P(A)]/P(R)
P(A|R) = 0.12/0.61 = 12/61

Is this correct so far? How do i go about working out part (iii)?

It looks good so far.

For (iii) you want $P\left( {A|R_1 R_2 } \right)$.
That can be done just as you did parts (i) & (ii).
It just is a bit more tedious.
• May 22nd 2011, 08:08 AM
Mcoolta
How do i go about finding the probability of R2, since i havent been told how many sweets are in the bag?

Thanks for your help so far.
• May 22nd 2011, 08:18 AM
Plato
Quote:

Originally Posted by Mcoolta
How do i go about finding the probability of R2, since i havent been told how many sweets are in the bag?

We have to make some assumptions here.
Let's assume there are 100 pieces in each bag.
So a bag from machine A has 40 reds.
If you are not comfortable with that, then you must ask the author about it.