Conditional Probability

[brandy]

Homework Statement

romeo proposed to juliet. now he's 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?

Homework Equations

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

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 I am 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.

 

[Ray Vickson]

Homework Statement

romeo proposed to juliet. now he's 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?

Homework Equations

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

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 I am 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.

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

RGV

 

[brandy]

i just did P(R∧Mon | W) + P(R∧Mon| Wˉ) = 0.2+0.05=0.25
so, this isn't right?

 

[Ray Vickson]

i just did P(R∧Mon | W) + P(R∧Mon| Wˉ) = 0.2+0.05=0.25
so, this isn't right?

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

RGV