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Probability

The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.

14,643 Questions

What are the possible outcomes when a die is rolled?

If a normal die is rolled once, the outcomes are {1, 2, 3, 4, 5, 6}.

What is the probability that a gaussian probability density function will take a value less than -2?

Assuming that you are considering a N(0,1) Gaussian distribution, the answer is approximately 1 in 20. The 0.95%ile (two tailed) occurs at -1.96 and 1.96.

One letter is randomly selected from the word math and a second letter is randomly selected from the word jokes what is the probability that both letters are vowels?

Word 1) 'math' has one vowel letter among a total of 4 letters. The probability of

randomly selecting the vowel letter 'a' is P(v) = 1/4.

Word 2) 'jokes' has two vowel letters among a total of 5 letters. The probability of

randomly selecting a vowel letter is P(v) = 2/5.

The probability of randomly selecting a vowel letter from the first word and a vowel

letter from the second word is: P(v1,v2) = 1/4 (2/5) = 2/20 = 1/10 = 0.10 = 10.0%

If X is a normal random variable with standard deviation 4.00 and if the probability that X is more than 5.52 is 0.305 then what is the mean of X?

Denote by mu the mean of X. Given

P(X>5.52)=0.305

i.e.,

P((X-mu)/4> (5.52-mu)/4)=0.305

So, letting Z=(X-mu)/4. Then Z~N(0,1). Hence, the above equality is

P(Z>(5.52-mu)/4)=0.305. So,

(5.52-mu)/4=0.51

So,

mu=5.52-4*0.51=3.48

So, the best answer is 3.5

There are 6 numbers on a normal dice What is the probability that if you roll the dice you'll get the number 100?

Since the numbers (number of dots) on normal dice only go from 1 - 6, then I would think the probability of getting the number 100 is zero.

There are 36 different outcomes possible when you toss two dice. What is the probability that the two dice will show the same number?

There are 6 different doubles that can be rolled. (They are 1 and 1, 2 and 2, etc.) You have a 6/36 chance of rolling doubles. The fraction 6/36 simplifies (reduces) to 1/6. Your 1 in 6 chance of rolling doubles now needs to be converted to probability. Probability speaks to the "chance" that something will occur. It is expressed as a "pure" number, and the range of probability is from 0 to 1. The probability 0 means that it cannot occur, and the probability 1 means that it will or must occur. Everything else falls in between. If you have a 1 in 6 chance of rolling doubles that translates into a 1 divided by 6 probability, or a 0.1666666... probability that a double will come up.

Why can't the probability of an event occurring be greater than 1?

If probability becomes greater than one, then the uncertainty coefficient fluctuates and results in a terminal case.

If two fair dice are rolled what is the probability of rolling a double given that the sum was 11?

Let A = rolling a double Let B = sum is 11 P(A)=6/36=1/6 P(B)=2/36=1/18 since (5,6) and (6,5) produce a sum of 11. We want to find P(A/B)= P(A & B) / P(B) = 0 / P(B)=0 P(A & B) represent the event getting a double and the sum being 11.

Probability of heads in a coin toss?

1/2 Because there is one side with heads (1/) and the total sides (/2)

What are all the possible outcomes for flipping or tossing three coins a dime a nickel and a penny in an organized manner and how would a tree diagram show these results?

There are eight possible results when flipping three coins (eliminating the highly unlikely scenario of one or more coins landing on their edge): Dime - Heads / Nickel - Heads / Penny - Heads Dime - Heads / Nickel - Heads / Penny - Tails Dime - Heads / Nickel - Tails / Penny - Heads Dime - Heads / Nickel - Tails / Penny - Tails Dime - Tails / Nickel - Heads / Penny - Heads Dime - Tails / Nickel - Heads / Penny - Tails Dime - Tails / Nickel - Tails / Penny - Heads Dime - Tails / Nickel - Tails / Penny - Tails

What is the shape of this distribution?

A company is studying the number of daily debit card purchases. If there were 20 purchases and the probability of a debit card purchase is 0.5

What is the shape of this distribution

What is the probability that a 3-digit positive integer picked at random will have one or more 7 in its digits?

A three digit number can be chosen in 9*10*10 = 900ways

No. of ways to choose a three digit number without 7 is 8*9*9 = 648 ways

probability of picking a three digit number that includes atleast one digit that is 7 is 1- (648/900) = 252/900 = 7/25

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