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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

How many ways can a group of 12 including 4 boys and 8 girls be formed into two 6 person volleyball teams with no restrictions?

462 ways
Explanation

In the question, it does not seem to matter how many boys or girls are on a team. So really you are asking how many ways are there to divide 12 people into two teams of 6.

The answer is (12C6)/2 where 12C6 means 12 choose 6

First 12 chose 6 is 12!/(12-6)!(6)! which is 12x11x10x9x8x7x6x5x4x3x2x1/(6x5x4x3x2x1)(6x5x4x3x2x1)=
(12x11x10x9x8x7)/(6x5x4x3x2x1)=924


(As a side note, the Google browser will calculate these numbers if you just type in 12 choose 6, for example)

Now once one team of 6 is chosen, the other team is automatically the remaining 6 so we have really double counted. That is why we divide by 2 and the answer
is 462 ways.

How do find the probability of distribution Let Y equals X1 - X2 plus 2x3 Find Pr Y1.5?

This question can only be answered if the probability distribution functions of X1, X2 and X3 are known. They are not and so the question cannot be answered.

How many tons of asphalt in a squaremeter?

Any number that you like: it depends how high the asphalt is stacked!

How many sets of color in a 52 card poker playing deck?

There are two colors, black and red, in a standard deck of cards used to play poker.

There are 26 red cards (13 hearts and 13 diamonds) and 26 black cards (13 spades and 13 clubs) in an ordinary deck.

Is it more likely for a coin to end on heads or tails?

The probability of a fair coin landing on heads or tails is even, i.e. 50/50.

How does probability help explain the results of a genetic cross?

Genetics often involves dominant and recessive alleles. For instance, blue eyes are recessive and brown eyes are dominant.1 Each parent contributes one allele. If you get two blues, then your eyes are blue. If you get one or two browns, then you eyes are brown. That means that, given a random contribution from your parents, you have a 25% probability of blue eyes.

It also means that, even though you have brown eyes, you could be carrying the blue allele, and two parents with brown eyes could have a blue eyed child.

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1Its more complicated than that, since eye color is actually polygenic, involving more than one allele. This example was simplified to answer the question.

What is the probability of rolling an odd number or an even number on a number cube?

A standard number cube has numbers 1-6, so there's a 50% (or one-half) chance of rolling both an odd or even number.

What is the probability of drawing a card from each of four decks and getting same card from all decks?

The probability of drawing some card from the first deck is 1 in 1. The probability of matching that card in the remaining three decks in 1 in 52 for each. Simply multiply 1/1 by 1/52 by 1/52 by 1/52 and you get 1 in 140608.

What is the formula for calculating the birthday paradox?

In a room of just 23 people there's a 50-50 chance of two people having the same birthday. In a room of 75 there's a 99.9% chance of two people matching birth dates.

What is the probability of choosing a jack or a queen from a standard deck of 52 cards?

The probability of drawing a jack or a queen from a standard deck of 52 cards is ((1 + 1) times 4 ) in 52, which is 8 in 52, or about 0.1538.

How many black eights are in a standard card deck?

There are two cards which ahve a value of eight which are black (spades and clubs). Each of these cards has two black numeral eights (8) for four black numeral eights in the deck

Whats the probability that you will die of cancer?

iam not saying this is not a good way of finding out things this way you'd get worried and some people lie on this website so ask your own doctor and see what he says!!

True or False A sampling distribution is a probability distribution for a statistic?

The statement is true that a sampling distribution is a probability distribution for a statistic.

What is the probability of getting an even number and a head when rolling a die and then tossing a coin?

These are unrelated events, so simply multiply them. 3 in 6, or 0.5 for the die, and 1 in 2, or 0.5 for the coin, multiplied together gives you 0.25.

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