Answer:
a. [tex]P (R3 | G1)=\frac{1}{5}[/tex]
b. [tex]P (R6| G3)= \frac{1}{3}[/tex]
c. [tex]P(G3|E)=\frac{2}{3}[/tex]
d. [tex]P (E|G3)=\frac{2}{3}[/tex]
Step-by-step explanation:
The sample space associated with the random experiment of throwing a dice is is the equiprobable space {R1, R2, R3, R4, R5, R6}. Then,
a. The conditional probability that 3 is rolled given that the roll is greater than 1? [tex]P (R3 | G1) = \frac{P (R3\bigcap G1)}{P(G1)} = \frac{1/6}{5/6} = \frac{1}{5}[/tex]
b. What is the conditional probability that 6 is rolled given that the roll is greater than 3? [tex]P (R6| G3) = \frac{P (R6\bigcap G3)}{P(G3)} = \frac{1/6}{3/6} = \frac{1}{3}[/tex]
c. What is P [GIE], the conditional probability that the roll is greater than 3 given that the roll is even? [tex]P(G3|E) = \frac{P (G3\bigcap E)}{P(E)} = \frac{2/6}{3/6} = \frac{2}{3}[/tex]
d. Given that the roll is greater than 3, what is the conditional probability that the roll is even? [tex]P (E|G3) = \frac{P (E\bigcap G3)}{P(G3)} = \frac{2/6}{3/6} = \frac{2}{3}[/tex]
