(Conditional Probability; Finite Stochastic Processes). A fair 20-faced die which has 5 red, 11 green, and 4 blue faces is tossed. If a red face appears, a fair 4-faced die (with numbers 1, 2, 3, 4 on the faces) is tossed; if a green face appears, a fair 6-faced die (with numbers 1, 2, ..., 6 on the faces) is tossed; if a blue face appears, a fair 12-faced die (with numbers 1, 2, ..., 12 on the faces) is tossed. (1) Determine each of the following probabilities: (a) a red face and a prime number appear (after a toss of the 20-faced die followed by a toss of the 4-faced die; here and below, please enter a rational num m/n in reduced form): (b) a green face and a prime number appear:
(Conditional Probability; Finite Stochastic Processes). A fair 20-faced die which has 5 red, 11 green, and 4 blue faces is tossed. If a red face appears, a fair 4-faced die (with numbers 1, 2, 3, 4 on the faces) is tossed; if a green face appears, a fair 6-faced die (with numbers 1, 2, ..., 6 on the faces) is tossed; if a blue face appears, a fair 12-faced die (with numbers 1, 2, ..., 12 on the faces) is tossed. (1) Determine each of the following probabilities: (a) a red face and a prime number appear (after a toss of the 20-faced die followed by a toss of the 4-faced die; here and below, please enter a rational num m/n in reduced form): (b) a green face and a prime number appear:
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:(Conditional Probability; Finite Stochastic Processes). A fair 20-faced die which has 5 red, 11 green, and 4 blue faces is tossed.
If a red face appears, a fair 4-faced die (with numbers 1, 2, 3, 4 on the faces) is tossed;
if a green face appears, a fair 6-faced die (with numbers 1, 2, ..., 6 on the faces) is tossed;
if a blue face appears, a fair 12-faced die (with numbers 1, 2, ..., 12 on the faces) is tossed.
(i) Determine each of the following probabilities:
(a) a red face and a prime number appear (after a toss of the 20-faced die followed by a toss of the 4-faced die; here and below, please enter a rational number
m/n in reduced form):
(b) a green face and a prime number appear:
(c) a blue face and a prime number appear:
(ii) Find the probability that a prime number appears:
(iii) Suppose that a prime number appears. Find the probability that a green face appeared in the preceding toss of the 20-faced die:
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