1. ## Probability of receiving a reply

Letters are sent by post and the probability that they are delivered in days are:
days: 1 2 3
1st class: 0.9 0.1 0
2nd class: 0.1 0.6 0.3
A secretary sends 4 letters and the receivers reply to them immediately on the same class mail. find the probability of receiving at least two replies within three days using second class post?
P(reply in 3 days)=$\displaystyle 0.1\times 0.1+2\times 0.1\times 0.6=0.13$
P(1 reply in 3 days)=$\displaystyle 0.13\times (0.87)^{3}=0.0856$
P(no replies in 3 days)=$\displaystyle 0.87^4=0.573$
P(at least 2 replies)=$\displaystyle 1-(0.0856+0.573)=0.341$
What have i done wrong? I have spent quite some time over it and can't see where i have missed anything
Thanks

2. Originally Posted by arze
Letters are sent by post and the probability that they are delivered in days are:
days: 1 2 3
1st class: 0.9 0.1 0
2nd class: 0.1 0.6 0.3
A secretary sends 4 letters and the receivers reply to them immediately on the same class mail. find the probability of receiving at least two replies within three days using second class post?
P(reply in 3 days)=$\displaystyle 0.1\times 0.1+2\times 0/1\times 0.6=0.13$ <= did you mean 2*0.1*0.6?
P(1 reply in 3 days)=$\displaystyle 0.13\times (0.87)^{3}=0.0856$
P(no replies in 3 days)=$\displaystyle 0.87^4=0.573$
P(at least 2 replies)=$\displaystyle 1-(0.0856+0.573)=0.341$
What have i done wrong? I have spent quite some time over it and can't see where i have missed anything
Thanks
What does that mean?

3. sorry typing error, i have edited it

4. Originally Posted by arze
Letters are sent by post and the probability that they are delivered in days are:
days: 1 2 3
1st class: 0.9 0.1 0
2nd class: 0.1 0.6 0.3
A secretary sends 4 letters and the receivers reply to them immediately on the same class mail. find the probability of receiving at least two replies within three days using second class post?
P(reply in 3 days)=$\displaystyle 0.1\times 0.1+2\times 0.1\times 0.6=0.13$
P(1 reply in 3 days)=$\displaystyle 0.13\times (0.87)^{3}=0.0856$ this is the probability of a reply to only one specific letter
P(no replies in 3 days)=$\displaystyle 0.87^4=0.573$
P(at least 2 replies)=$\displaystyle 1-(0.0856+0.573)=0.341$
What have i done wrong? I have spent quite some time over it and can't see where i have missed anything
Thanks
P(reply to 1st letter)=$\displaystyle (0.13)0.87^3$

P(reply to 2nd letter)=$\displaystyle (0.13)0.87^3$

P(reply to 3rd letter)=$\displaystyle (0.13)0.87^3$

P(reply to 4th letter)=$\displaystyle (0.13)0.87^3$

P(no replies)=$\displaystyle 0.87^4$

P(at most 1 reply)=$\displaystyle 4[(0.13)0.87^3]+0.87^4=0.573+0.342=0.915$

P(at least 2 replies)=$\displaystyle 1-0.915=0.085$