# Conditional Probability

#### brandy

1. Homework Statement
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. Homework 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.

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#### Ray Vickson

Homework Helper
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1. Homework Statement
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. Homework 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.
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 isnt right???