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Chapter 3: Q.3.8 (page 98)
A couple has children. What is the probability that both are girls if the older of the two is a girl ?
is the probability that both are girls if the older of the two is a girl.
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In Example , suppose that the new evidence is subject to different possible interpretations and in fact shows only that it is percent likely that the criminal possesses the characteristic in question. In this case, how likely would it be that the suspect is guilty (assuming, as before, that he has the characteristic)?
A red die, a blue die, and a yellow die (all six-sided) are rolled. We are interested in the probability that the number appearing on the blue die is less than that appearing on the yellow die, which is less than that appearing on the red die. That is, with B, Y, and R denoting, respectively, the number appearing on the blue, yellow, and red die, we are interested in .
(a) What is the probability that no two of the dice land on the same number?
(b) Given that no two of the dice land on the same number, what is the conditional probability that ?
(c) What is ?
If two fair dice are rolled, what is the conditional probability that the first one lands on 6 given that the sum of the dice is ? Compute for all values of between and
You ask your neighbor to water a sickly plant while you are on vacation. Without water, it will die with probability .; with water, it will die with probability .. You are percent certain that your neighbor will remember to water the plant.
(a) What is the probability that the plant will be alive when you return?
(b) If the plant is dead upon your return, what is the probability that your neighbor forgot to water it?
A coin having probability .of landing on heads is flipped. A observes the result鈥攅ither heads or tails鈥攁nd rushes off to tell . However, with probability ., 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 that the coin landed on heads or that it landed tails. (If he does remember, then he tells the correct result.)
(a) What is the probability that is told that the coin landed on heads?
(b) What is the probability that is told the correct result?
(c) Given that is told that the coin landed on heads, what is the probability that it did in fact land on heads?
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