# Need your help in probability problems? Thanks :)

##### 2 Answers

See below

#### Explanation:

P(x)=

P(Y)=

P(X nn Y)

P(X uu Y)

The sample space would be the numbers 1 to 12

The events are dependent as 1 and 3 are in both events

Given event A has occurred P(even)=

Sorry don't know what P(X/Y) means

**What is **#"P"(X)# ?

The probability of event

#"P"(X)="the number of elements in X"/"the number of elements in S"#

Since there are 12 possible rolls,

#"P"(X)=8/12#

#color(white)("P"(X)) = 2/3#

**What is **#"P"(Y)# ?

Similarly,

#"P"(Y)=5/12#

**What is **#"P"(X nn Y)# ?

The event

#"P"(XnnY) = 2/12#

#color(white)("P"(XnnY)) = 1/6#

**What is **#"P"(XuuY)# ?

The event

By observation, we see

#"P"(XuuY) = 11/12#

**Write down the sample space **#S# of possible outcomes.

#S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}#

**Are **#X# and #Y# independent? Explain.

Two events

#"P"(XnnY) = "P"(X) xx "P"(Y)#

From above, we know

#1/6 stackrel"? "= 2/3 xx 5/12=(1xx5)/(3xx6)=5/18 != 1/6#

Since

**What is the probability that you rolled an even number, given that event **#A# has occurred?

There is no event

#"P"("even"|X)= "the number of even numbers in X"/"the size of X"#

Event

#"P"("even"|X)= 2/8#

#color(white)("P"("even"|X))= 1/4#

**What is **#"P"(X|Y)# ?

Similarly,

#"P"(X|Y) =("the size of X "nn" Y")/"the size of Y"= ("P"(X nn Y))/("P"(Y))#

#color(white)("P"(X|Y)) = 2/5#