Solution Found!
A coin having probability .8 of landing on heads is
Chapter 3, Problem 14STE(choose chapter or problem)
Problem 14STE
A coin having probability .8 of landing on heads is flipped. A observes the result—either heads or tails —and rushes off to tell B. However, with probability .4, A will have forgotten the result by the time he reaches B. If A has forgotten, then, rather than admitting this to B, he is equally likely to tell B that the coin landed on heads or that it landed tails. (If he does remember, then he tells B the correct result.)
(a) What is the probability that B is told that the coin landed on heads?
(b) What is the probability that B is told the correct result?
(c) Given that B is told that the coin landed on heads, what is the probability that it did in fact land on heads?
Questions & Answers
QUESTION:
Problem 14STE
A coin having probability .8 of landing on heads is flipped. A observes the result—either heads or tails —and rushes off to tell B. However, with probability .4, A will have forgotten the result by the time he reaches B. If A has forgotten, then, rather than admitting this to B, he is equally likely to tell B that the coin landed on heads or that it landed tails. (If he does remember, then he tells B the correct result.)
(a) What is the probability that B is told that the coin landed on heads?
(b) What is the probability that B is told the correct result?
(c) Given that B is told that the coin landed on heads, what is the probability that it did in fact land on heads?
ANSWER:
Step 1 of 4
Let H = event that the coin lands head.
= the event that B is told that the coin landed heads
F = the event that A forgets the result of the toss,
C = the event that B is told the correct result.
P(F) = 0.4, P() = 0.6, P(H) = 0.8, and P(
/F) P(F) = 0.5