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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

According to the normal probability distribution 95 percent of the values of a normal random variable are contained w in plus or minus how many standard deviations from the mean Why is that important?

Approximately 2 standard deviations (1.96, actually) from the mean. That is important to know that if one has a sample of 1000 values, if one selects a threshold at +/- 2 standard deviations from the mean, then one expects to see about 25 values exceeding those thresholds (on each side of the mean)

What's the probability of tossing a 6-sided die three times and getting an even number all three times?

Each time you toss the die the probability of rolling an even number is 3 out of 6 or 1/2. So, the probability of tossing three consecutive even numbers is (1/2)3 = 1/8 = 0.125, which is one chance in eight.

Event A has probability 0.4 event B has probability 0.5 If A and B are disjoint then the probability that both events occur is?

If two events are disjoint, they cannot occur at the same time. For example, if you flip a coin, you cannot get heads AND tails. Since A and B are disjoint, P(A and B) = 0

If A and B were independent, then P(A and B) = 0.4*0.5=0.2. For example, the chances you throw a dice and it lands on 1 AND the chances you flip a coin and it land on heads. These events are independent...the outcome of one event does not affect the outcome of the other.

Where probability is used today?

Weather forecasts, engineering, sales and advertising, etc. It is used very often when risk or potential volume must be determined, such as in size of streets for future development, or buying and selling of goods. Probability also has a large role in quantum physics.

Among the contestants in a competition are 49 women and 29 men so if 5 winners are randomly selected what is the probability that they are all men?

(29/78)*(28/77)*(27/76)*(26/75)*(25/74) = .0056252425

two events are dependent if the outcome of one event affects the probability of the other events. The probability that dependent events A and B occur together is

P(A and B) = P(A) * P(B given A)

The Staff at a small company includes 4 secretaries 20 technicians 4 engineers 2 executives and 50 workers. If a person is selected at random what is the probabilty that he or she is a factory worker?

secretaries......4

technicians...20

engineers...... 4

executives......2

workers........50

==========

Total............80

Probability to select a factory worker = 50/80 or 5/8

A die is thrown Fine the probability that the dots on the top are even numbers or odd numbers?

in the equation system f/d = p where f is the number of sides of the rolled polyhedron which contain a number of spots that can be represented by a positive integer not divisible by 2 and d represents the total number of faces of the polyhedron which can, in the rest position, face upward, the variable p represents the probability of rolling an odd number. from this it can also be derived that the probability p of rolling an even number can be represented by (d-f)/d.

What is the probability of wiring a three phase motor rotation right the first time?

Since it can only rotate two directions, the chance is 50%. There are rotation indicators you can buy to check the phase sequence.

If a single die is rolled 6 times what is the probability of getting at least on 3?

You must first look at all possible outcomes:

1, 2, 3, 4, 5, 6

Then, reread the question that is being asked:

A dice is rolled 6 times, what is the probability of getting atleast a 3.

You should underline the important parts of the question and then preceed to answering:

When the question states, atleast a 3, it means to say the minimum result of 3 (as in 3, 4, 5 and 6)

The math:

(Outcomes that satisfy the statement)/(Total outcomes) * 100

We multiply by 100 to receive a percentage.

4/6 * 100 = 66.67%

The answer:

The probability of getting atleast a 3 when a dice is rolled 6 times is 66.67%.

What is the probability of getting head lice and how do you stop yourself from being scared of getting head lice?

If you have primary school age children then the likelihood of them getting head lice (repeatedly!( these days is very high - believe me! Chances are you will have them too at some point. Other than that, I would think your chances of catching them are quite low.

To stop yourself being scared the best thing to do is to realise that it happens to lots of normal people, and to lots of normal people's children. You get a more realistic picture when you realise that - it is not a major catastrophe, nor something that can't be fixed. They can even be eradicated naturally - it just takes patient combing with a fine tooth comb - for a few weeks to ensure none are left.

One way to keep them away, there is home remedy.. it conset of rosemary poppuri a lil of olive oil, (because you don't want to dry out the sclap with the poppuri) so u mix it all up! apply around the edges of the hair. where lice tend to enter.. for sum reason the lice don't like it... so there u have it good luck.. if this works for u let me no!! muah...

Why be scared lol it happens you just need to get the right stuff to put on your hair.... and...... bobs your uncle!!!!! well he's my dad but you get my point

How many 9 digit combinations are there for the numbers 1 through 9?

9 times 9 times 9 times 9 times 9 times 9 times 9 times 9 times 9 =

Imagine it's a combination lock with 9 tumblers. Each tumbler has 9 "positions" - the digits from 1 to 9. So you multiply the number of digits [9] against itself [9] for as many tumblers are in the combination (9).

Tumbler # 1 2 3 4 5 6 7 8 9

Number of

possible

digits 9 9 9 9 9 9 9 9 9

What is the probability of having twins if your dad is a twin?

I'm not sure on the actual percentages. It firstly depends on if your father is an identical or non-identical twin. (Maternal or fraternal) Non-identical (fraternal) twins are the hereditary type, not the identical ones. Identical twins are simply a hiccup with the cell division during fetal growth, whereas non-identical twins are due to the hereditary tendency of the woman releasing more than one egg at a time. The gene for non-identical twins is directly passed from fathers to daughters, and the chance of having twins usually skips a generation too (like baldness in men!). So, if your father is a twin (a non-identical twin) and you are his daughter, it's possible that you may also have twins, but it's far more likely that your daughter will. My father is a twin (his brother died at birth and it's not known if he was maternal or fraternal unfortunately) and I only have 1 child (a daughter). She has a very high chance of having twins if dad was fraternal.

What is the probability that you will roll a number less than 3 and flip heads if you roll a six-sided die and toss a coin?

1 and 2 are the only two numbers less than 3 so the odds of rolling a number less than 3 is 2/6 or 1/3. Now the odds of heads is 1/2. We use the multiplication rule and we have

1/2x 1/3=1/6 so the odd are 1 in 6

If four coins are tossed what is the probability of getting three heads and one tail?

With 4 coins you have 24 (16) possibilities. If we wanted a specific coin to land 'tails' while the others landed 'heads' we would have one possibilty out of 16. Since we don't care which of the coins lands 'tails,' we have four chances in 16 or a 25 percent chance.

Quadratic functions in real life?

  • The orbit of a satellite, planet, moon, or comet.
  • The interaction of a charged particle in the vicinity of the nucleus of an atom.
  • The trajectory of a baseball, bullet, or missile.
  • The dropping of a rock from a bridge.
  • Skydiving. (At least, up to terminal velocity.)
  • etc., etc., etc.

If a number from 1 to 20 is chosen what is the probability of getting 7?

1 out of 20

this is because there are 20 numbers in total, and there is only one 7 in there. (Assuming that there is the same probability for each number to be chosen, and that 17 is excluded as an affirmative outcome)

How can you be sure of getting the expected 50 50 ratio from flipping a coin?

You can never be sure. The more often you toss it the closer the probability gets to a 50-50 split but there is no guarantee.

From an ordinary deck of 52 cards 26 red and 26 black 3 cards are drawn without replacement Using a tree diagram find the probability that all the cards drawn are black?

Using a tree diagram to solve this is using a sledge-hammer to crack a nut. the answer is (26/52 )(25/51)(24/50) or 6/51 = 2 / 17

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