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drek231 [11]
3 years ago
6

You have a six-sided die that you roll once. Let Ri denote the event that the roll is i. Let G j denote the event that the roll

is greater than j. Let E denote the event that the roll of the die is even-numbered.
(a) What is P[RsIG1], the conditional probability that 3 is rolled given that the roll is greater than 1?
(b) What is the conditional probability that 6 is rolled given that the roll is greater than 3?
(c) What is P[GIE], the conditional probability that the roll is greater than 3 given that the roll is even?
(d) Given that the roll is greater than 3, what is the conditional probability that the roll is even?
Mathematics
1 answer:
Misha Larkins [42]3 years ago
6 0

Answer:

a. P (R3 | G1)=\frac{1}{5}

b. P (R6| G3)= \frac{1}{3}

c. P(G3|E)=\frac{2}{3}

d. P (E|G3)=\frac{2}{3}

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? P (R3 | G1) = \frac{P (R3\bigcap G1)}{P(G1)} = \frac{1/6}{5/6} = \frac{1}{5}

b. What is the conditional probability that 6 is rolled given that the roll is greater than 3? P (R6| G3) = \frac{P (R6\bigcap G3)}{P(G3)} = \frac{1/6}{3/6} = \frac{1}{3}

c. What is P [GIE], the conditional probability that the roll is greater than 3 given that the roll is even? P(G3|E) = \frac{P (G3\bigcap E)}{P(E)} = \frac{2/6}{3/6} = \frac{2}{3}

d. Given that the roll is greater than 3, what is the conditional probability that the roll is even? P (E|G3) = \frac{P (E\bigcap G3)}{P(G3)} = \frac{2/6}{3/6} = \frac{2}{3}

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