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?

a) 0.68

b) 0.8

c) 0.8

Step-by-step explanation:

The probability that the coin lands on heads and A does not forget is: 0.8 x 0.6 = 0.48The probability that the coin lands on tails and A does not forget is similarly:                                                                                                         0.2 x 0.6 = 0.12The probability of A forgetting the result and telling B it's heads is:         0.4 x 0.5 = 0.2                                                                                              (This probability is the same as when A forgets and tells B it's tails too.)

Using these results lets answer parts (a) through (c):

a) The probability that B is told it landed on heads is going to be 0.48 + 0.2. This takes into account scenario 1, and 3 where A tells B the result is heads.

b) The probability that B is told the correct answer is 0.48 + 0.12 + (the probability A is correct when telling B the result after forgetting). For this, we need to consider scenario 3, and multiply it with the probability of being right.

For heads, this is: 0.2 x 0.8 = 0.16

For tails, this is: 0.2 x 0.2 = 0.04

Finally, the probability B is told the correct answer is:

0.48 + 0.12 + 0.16 + 0.04 = 0.8

c) Since it is stated that B is told the coin landed on heads, we do not need to consider whether A is telling the truth or not. We only need to state the probability of getting heads when the coin is flipped. Thus this answer is 0.8.

Where is the diagram?

5would be the answer- explanation