A red and a blue die are thrown. Both dice are fair (that is, all sides are equally likely). The events , , and are defined as follows: : The sum of the numbers on the two dice is at most 3. : The sum of the numbers on the two dice is odd. : The number on the red die is 3. a. Calculate the probability of each individual event; that is, calculate (), (), and ().
b. What is (|)?
c. What is (|)?
d. What is (|)?
e. Consider all pairs of events: and , and , and and . Which pairs of events are independent?
My attempt
a) $p(A)=\frac { 3 }{ 36 } $=$\frac { 1 }{ 13 } $
$p(B)=\frac { 18 }{ 36 } $=$\frac { 1 }{ 1 } $
$p(C)=\frac { 1 }{ 6 } $
b) (|) = $\frac{P(A\cap B)}{p(B)}$ = $\frac{\frac { 1 }{ 18 }}{\frac { 1 }{ 2 }}$ = $\frac { 1 }{ 9 } $
c) (|) = $\frac{P(B\cap C)}{p(C)}$ = $\frac{\frac { 1 }{ 12 }}{\frac { 1 }{ 6 }}$ = $\frac { 1 }{ 2 } $
d) (|) = $\frac{P(A\cap C)}{p(C)}$ = 0. because there is no common for A and C.
can anyone verify this..
Parts a,b,c,d all look good so far. For part e) just check either
$Pr(A|B)=Pr(A)$ or $Pr(A \cap B)=Pr(A)\cdot Pr(B)$
Hope this helps