Probability

It means the two events cannot simultaneously occur; for example the two events, being dead and being alive are mutually exclusive, since they cannot occur at the same time.

gregor mendel

True.

If the odd favoring an event are 10 to 1, then the probability of the event occurring is 0.9.

The odds in favor of an event are 10:1.

Find the probability that the event will occur.

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P(E)+P(E') = 1

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P(E)/P(E') = 10/1

So P(E) = 10P(E')

----

Substitute for P(E) and solve for P(E'):

10P(E')+P(E') = 1

11P(E') = 1

P(E') = 1/11

---

Therefore P(E) = 10/11

35:1 or 35 to 1.

"Snake eyes"

The probability for a total of two on two dice are the product of the chances

on each die. You will get one spot an average of one time in six on

one die, so the chances are one in 6. The same is true on the second

die, so the chance of both happening together on one roll are 1/6 x 1/6

or 1/36.

"On average,"1 out of 36 times you will get "snake eyes," so 35 out

of 36 times you will not.

That make the odds AGAINST equal 35:1 or 35 to one.

Answer: 17 to 1

Out of 36 possibilities for two dice, a total of three

can be made by

1 + 2 OR

2 +1

That makes the chances FOR equal to 1/36 plus 1/36, or 2/36 or 1 in 18 throws.

The odds against are therefore 17 to 1.

"On the average," you will 17 non-threes for each three.

Assuming that the die is a "normal" one (it has the numbers 1 to 6 and that it is fair), then the probability of rolling six three times in a row is 1/6*1/6*1/6 = 1/216 = 0.00463

The probability of rolling six three times in a row eventually is 1 (ie a certainty).

I am guessing that a theoretical assertion is made when one states something that is not fact as if it were fact.

More than you'd believe! The first book can be any one of twenty, the second any one of the remaining nineteen and so on until the fifteenth book can be any of the last six.

This is 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 different arrangements, which multiplies to a 17-digit number!

20,274,183,401,472,000 or "twenty quadrillion, two hundred and seventy four trillion, one hundred and eighty three billion, four hundred and one million, four hundred and seventy two thousand" (in US figures).

Do not attempt to check it in your local library!

Probability = number_of_white_marbles / total_number_of_marbles

= 10 / (4 + 6 + 4 + 10)

= 10 / 24

= 5/12

~= 0.42

The first dice can show any number. However the second dice has a 1 in 6 chance of being the same as the first.

Hence the probability of getting two numbers the same is 1/6.

24 red marbles

Flipping a coin is a 50-50 chance no decision or thought needed. A jury should have the right of mind not to base a conviction on luck they have to decide for themselves and weight the options. It is not a just process to take the lives of others in the hands of chance.

22 marbles are in the fifth line.

The day you are born is a specific event.

The probability of tossing a coin 9 times and getting at least one tail is:

P(9 times, at least 1 tail) = 1 - P(9 heads) = 1 - (0.50)9 = 0.9980... ≈ 99.8%

There are two screws located under the bottom sticky pad that hold down the silver face plate. Push on the pad with your finger until you see two dimples and then insert a small Philips screwdriver to unscrew the screws.

Unfortuantely, there is not much you can repair in the control pod except for a broken solder joint or a torn wire.

The probability of rolling a 7 at any time on a single die is zero.

30 ways.

Standard error is random error, represented by a standard deviation. Sampling error is systematic error, represented by a bias in the mean.

Bradford Services Inc. (BSI) is considering a project that has a cost of $10 million and an expected life of 3 years. There is a 30 percent probability of good conditions, in which case the project will provide a cash flow of $9 million at the end of each year for 3 years. There is a 40 percent probability of medium conditions, in which case the annual cash flows will be $4 million, and there is a 30 percent probability of bad conditions and a cash flow of -$1 million per year. BSI uses a 12 percent cost of capital to evaluate projects like this.

a. Find the project\'s expected cash flows and NPV.

b. Now suppose the BSI can abandon the project at the end of the first year by selling it for $6 million. BSI will still receive the Year 1 cash flows, but will receive no cash flows in subsequent years. Assume the salvage value is risky and should be discounted at the WACC.

c. Now assume that the project cannot be shut down. However, expertise gained by taking it on will lead to an opportunity at the end of Year 3 to undertake a venture that would have the same cost as the original project, and the new project\'s cash flows would follow whichever branch resulted for the original project. In other words, there would be a second $10 million cost at the end of Year 3, and then cash flows of either $9 million, $4 million, or -$1million for the following 3 years. Use decision tree analysis to estimate the value of the project, including the opportunity to implement the new project in Year 3. Assume the $10 million cost at Year 3 is known with certainty and should be discounted at the risk-free rate of 6 percent. Hint: do one decision tree for the operating cash flows and one for the cost of the project, then sum their NPVs.

d. Now suppose the original (no abandonment and no additional growth) project could be delayed a year. All the cash flows would remain unchanged, but information obtained during that year would tell the company exactly which set of demand conditions existed. Use decision tree analysis to estimate the value of the project if it is delayed by 1 year. Hint: Discount the $10 million cost at the risk-free rate since it is known with certainty. Show two time lines, one for operating cash flows and one for the cost, then sum their NPVs.

e. Go back to part c. Instead of using decision tree analysis, use the Black-Scholes model to estimate the value of the growth option. The risk-free rate is 6 percent, and the variance of the project\'s rate of return is 22 percent.

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1/2 independent from temperature

They can't. If they are ME, then if you get one, you know that the other will not occur. By def of Indep. , knowing the outcome of an event cannot tell you info about the other.

Actually, that is not entirely true - in the (rather trivial) case that the probability of one event is zero - both conditions are met. It is false

Both are equivalent!

* Probability of using 50-50 and getting the right answer:

1/2

* Probability of using double dip and getting the right answer:

= Probability that either first or the second guess is correct

P(First guess is correct) = 1/4

+

P(First guess in wrong and second guess is correct) = 3/4 * 1/3 = 1/4

= 1/2

Ideally, the probability of getting any specific combination of length n is 0.5n = 1/2n. For n = 3, this is 0.125 = 1/8.