Three prisoners, A, B, and C, are held in separate cells. Two are to be executed. The warder knows

specifically who is to be executed, and who is to be freed, whereas the prisoners know only that two

are to be executed. Prisoner A reasons as follows: my probability of being freed is clearly 1

3

until I

receive further information. However, it is clear that at least one of B and C will be executed, so I

will ask the warder to name one prisoner other than myself who is to be executed. Once I know which

of B and C is to be executed, either I will go free or the other, unnamed, prisoner will go free, with

equal probability. Hence, by asking the name of another prisoner to be executed, I raise my chances

of survival from 1

3

to 1

2

. Investigate A's reasoning. [Hint: find the conditional probability that A is

freed, given that the warder names B to be executed.]

Given the accompanying information for a fanciful hero universe:

Flying Telepathy Super Strength

Female 97 92 77

Male 24 64 3

Dissemination of Super Power by Gender

What is the observational likelihood that a haphazardly chosen hero will have clairvoyance?

Answer in decimal structure. Round to 3 decimal places on a case by case basis

An overview asked 816 school green beans whether they had been to a film or eaten in a caf during the previous week. The accompanying data was acquired: 391 green beans had been to neither a film nor an eatery, and 266 had been to a film. In the event that 92 of the individuals who had been to a film had not been to a caf, what number of the reviewed green beans had been to the accompanying?

(a) both a film and a caf

(b) a film or a caf

(c) a caf

(d) a caf however not a film

A rescue vehicle goes to and fro, at a steady explicit speed v, along a street of length L. We may show the area of the emergency vehicle at any second on schedule to be consistently circulated over the span (0, L). Additionally at any second on schedule, a mishap (not including the emergency vehicle itself) happens at a point consistently disseminated out and about; that is, the mishaps distance from one of the fixed stopping points is likewise consistently conveyed over the stretch (0, L). Expect the area of the mishap and the area of the rescue vehicle are free.

Assuming the emergency vehicle is fit for guaranteed U-turns, register the CDF and PDF of the ambulances head out time T to the area of the mishap.

Alex Mason has a wide-bending, uphill carport prompting

~28~

his carport. When there is a weighty snow, Alex enlists a nearby

woodworker, who digging tools snow as an afterthought in the colder time of year, to

scoop his carport. The snow shoveler charges $30 to

scoop the carport. Following is a likelihood conveyance

of the quantity of hefty snows each winter.Alex is thinking about the acquisition of another self-pushed

snowblower for $575 that would permit him, his better half, or his

kids to clear the carport after a snow. Talk about what

you believe Alex's choice ought to be and why.

Weighty Snows Probability

1 1.12

2 0.19

3 0.24

4 0.22

5 0.13

6 0.08

7 0.02

3. The King of Fredonia drinks glasses of wine at a Poisson rate of 2 glasses per day. Assassins attempt to poison the king's wine glasses. There is a 0.02 probability that any given glass is poisoned. Assume that drinking poisoned wine is always fatal instantly and it is the only cause of death. In addition, the occurrence of poison in the glasses and the number of glasses drunk are independent events. What is the probability that the currently king survives as least 50 days?Given the following table which represents the daily requests for assistance from a poison control center, complete it so that it represents a probability distribution. Number of 0 2 3 5 6 Requests (X) Probability 0.1 0.1 0.17 0.05 0.1 0.1 a. Show this is a probability distribution. b. What is the probability that the number of requests is at least 2? c. P(X