• Example 2. Two students are working separately on the same problem. If the first student has probability of solving it and the second student has probability of solving it, what is the probability that at least one of them solves it? Let A be the event “first student succeeds," and B be the event "second student succeeds." Then P(AB) = ; = (assume A and B independent since the students work separately). Then by (3.6) the probability that one or the other or both students solve the problem is 1 Р(А+ B) — 3 7 8. Conditional Probability; Bayes' Formula If we are asked for the probability of event B assuming that event A occurs [that is, PA(B)], it is often useful to find it from (3.1): Р(АB) Р(А) (3.8) РА(В) — Equation (3.8) is called Bayes' formula. In any conditional probability problem to which the answer is not immediately obvious, you should consider whether you can easily find P(A) and P(AB); if so, the conditional probability PA(B) is given by (3.8).
• Example 2. Two students are working separately on the same problem. If the first student has probability of solving it and the second student has probability of solving it, what is the probability that at least one of them solves it? Let A be the event “first student succeeds," and B be the event "second student succeeds." Then P(AB) = ; = (assume A and B independent since the students work separately). Then by (3.6) the probability that one or the other or both students solve the problem is 1 Р(А+ B) — 3 7 8. Conditional Probability; Bayes' Formula If we are asked for the probability of event B assuming that event A occurs [that is, PA(B)], it is often useful to find it from (3.1): Р(АB) Р(А) (3.8) РА(В) — Equation (3.8) is called Bayes' formula. In any conditional probability problem to which the answer is not immediately obvious, you should consider whether you can easily find P(A) and P(AB); if so, the conditional probability PA(B) is given by (3.8).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![• Example 2. Two students are working separately on the same problem. If the first student
has probability of solving it and the second student has probability of solving
it, what is the probability that at least one of them solves it?
Let A be the event “first student succeeds," and B be the event "second student
succeeds." Then P(AB) = ; = (assume A and B independent since the
students work separately). Then by (3.6) the probability that one or the other or
both students solve the problem is
1
Р(А+ B) —
3
7
8.
Conditional Probability; Bayes' Formula If we are asked for the probability
of event B assuming that event A occurs [that is, PA(B)], it is often useful to find
it from (3.1):
Р(АB)
Р(А)
(3.8)
РА(В) —
Equation (3.8) is called Bayes' formula. In any conditional probability problem to
which the answer is not immediately obvious, you should consider whether you
can easily find P(A) and P(AB); if so, the conditional probability PA(B) is given
by (3.8).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ed6a8b1-6d1a-451b-8104-a4120031b3dd%2Fdda92cbd-3cc3-478e-8fab-9b5e453a202c%2Fx8yzu7b_processed.png&w=3840&q=75)
Transcribed Image Text:• Example 2. Two students are working separately on the same problem. If the first student
has probability of solving it and the second student has probability of solving
it, what is the probability that at least one of them solves it?
Let A be the event “first student succeeds," and B be the event "second student
succeeds." Then P(AB) = ; = (assume A and B independent since the
students work separately). Then by (3.6) the probability that one or the other or
both students solve the problem is
1
Р(А+ B) —
3
7
8.
Conditional Probability; Bayes' Formula If we are asked for the probability
of event B assuming that event A occurs [that is, PA(B)], it is often useful to find
it from (3.1):
Р(АB)
Р(А)
(3.8)
РА(В) —
Equation (3.8) is called Bayes' formula. In any conditional probability problem to
which the answer is not immediately obvious, you should consider whether you
can easily find P(A) and P(AB); if so, the conditional probability PA(B) is given
by (3.8).
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