# Conditional Probability

1. Aug 24, 2011

### brandy

1. The problem statement, all variables and given/known data
romeo proposed to juliet. now hes waiting for her response.
R = 'event that she replies'
W='event that she wants to get married'
Mon = 'event on monday'
Tue = 'event on Tuesday'

P(R$\wedge$Mon | W) = 0.2
P(R$\wedge$Tue | W) = 0.25
P(R$\wedge$Mon| $\bar{W}$) = 0.05
P(R$\wedge$Tue | $\bar{W}$) = 0.1
P(R|W) = 1.0
P(R|$\bar{W}$) = 0.7
P(W)=0.6

If Romeo has not received her reply on Monday, what is the probability that he will receive the letter on Tuesday?

2. Relevant equations
there are more probabilities for each day of the week for both W and bar W.

3. The attempt at a solution

I used to total probability to calculate P(R $\wedge$ Mon) = 0.25, and for tuesday = 0.35
and i believe what im trying to calculate now is P(R$\wedge$ Tue | $\bar{Mon}$) $\wedge$ W)

so far, because its too difficult to latex it all. i have applied bayes theorem, and i have tried fiddling around with all 4 of the given ones. I need some direction.

2. Aug 24, 2011

### Ray Vickson

What formulas did you use to get P{Mon & R} = 0.25, etc.? I get very different results.

RGV

3. Aug 31, 2011

### brandy

i just did P(R∧Mon | W) + P(R∧Mon| Wˉ) = 0.2+0.05=0.25
so, this isnt right???

4. Aug 31, 2011

### Ray Vickson

No. Go back and look in detail at Bayes' Theorem.

RGV