S1 Probability

a bag P contains 3 red balls. a second bag Q contains 2 red balls and 3 black balls.

i) a bag is chosen at random and one ball is withdrawn. find the probability that this ball is red (did this one, answer is 0.7)

this ball remains outside the bag.

ii) a bag is again chosen at random (it isnt known whether this is hte same bag as before or not) and one ball is withdrawn. find hte joint probability that both this ball and the one previously withdrawn are red.

iii) if they are both red, what is the probability that bag p was used on both occasions?

Reply 1

Tallon

I think you'd just have to laboriously go through all the different combinations of events happening I'm afraid. If it's hard to keep up with it, maybe draw yourself a tree diagram?

Reply 2

nota bene

(1/2)*(3/3)+(1/2)*(2/5)=1/2+1/5=7/10
ii)
if first ball drawn from bag P

if first ball drawn from bag Q

Consider these two separately

iii) Work backwards or use Bayes'

Reply 3

Tallon

nota bene

(1/2)*(3/3)+(1/2)*(2/5)=1/2+1/5=7/10
ii)
if first ball drawn from bag P

if first ball drawn from bag Q

Consider these two separately

Spoiler

iii) Work backwards or use Bayes'

Spoiler

Also, I think (iii) is a conditional probability isn't it? It's basically saying find the probability you get red in bag p twice given that you get red twice?

Reply 4

nota bene

Tallon

Spoiler

Lol, I shall not to probability work, I always mess up one possibility. I agree with that answer.

Also, I think (iii) is a conditional probability isn't it? It's basically saying find the probability you get red in bag p twice given that you get red twice?