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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 is the theoretical probability of randomly selecting a 3 child family with 3 girls?

The gender of children is not a constant. It depends on the parental predispositions - mainly on the father's genes but apparently the mother's age can also affect the gender. The details of these influences are not understood well enough to develop an accurate model.

If you make the simplistic but unjustified assumption that both genders are equally likely, the answer is 1/8.

Why two tail of normal distribution do not touch the horizontal axis?

The domain of the Normal distribution is the whole of the real line. As a result the horizontal axis is asymptotic to the Normal distribution curve. The curve gets closer and closer to the axis but never, ever reaches it.

What is the probability of rolling a sum of 8 on at least one of two rolls of a pair of number cubes?

The probability of rolling a sum of 8 on one roll of a pair of dice is 5/36.

The probability of not rolling a sum of 8 on one roll of a pair of dice is 31/36.

The probability of rolling a sum of 8 twice on two rolls of a pair of dice is

(5/36)(5/36) = (5/36)2 .

The probability of rolling first a sum of 8 and then rolling a sum that is not 8 on the

second roll is (5/36)(31/36).

The probability of rolling a sum that is not 8 on the first roll and rolling a sum of 8

in the second roll is (31/36)(5/36).

So The probability of rolling a sum of 8 at least one of two rolls of a pair of dice is

(5/36)2 + (5/36)(31/38) + (31/36)(5/36) = 0.258487654... ≈ 25.8%.

What is the difference between stratified and random sampling?

In a stratified sample, the sampling proportion is the same for each stratum. In a random sample it should be but, due to randomness, need not be.

What is the probability that a family of 2 children has no boys?

There is a One in two chance that the first child is a girl (not a boy), then there is the same chance (1/2) that the second child is not a boy. The chance that neither is a boy is (1/2) * (1/2) = 1/4.

Another way to look at it is like a table or grid. There are four possibilities, represented by the grid. The rows represent the sex of the first child, and the columns the second child. Where they intersect is the combination of the two. So you want any square where there are no boys (both girls). So there is only 1 square out of the 4 where this is true (denoted by a Y for Yes, the others denoted by n for no):

* | B | G |

B | n | n |

G | n | Y |

What is the probability of drawing a jack or queen or king?

The probability of drawing a jack is, P(J) = 1/13.

The probability of drawing a queen is, P(Q) = 1/13.

The probability of drawing a king is, P(K) = 1/13.

The probability of drawing a jack or drawing a queen or drawing a king is;

P(J or Q or K) = 1/13 + 1/13 + 1/13 = 3/13 = 0.23076923... ≈ 23.1%.

What are the uses of probability ratio?

With probability ratios the value you get to describe the strength of the relationship when you compare (A given B) to (A given not B) is not the same as what you get when you compare (not A given B) to (not A given not B). This is, IMHO, a big problem. There is no such problem with odds ratios.

How do you find the number z such that the proportion of observations that are less than z in a standard Normal distribution is 0.7?

You will need to use tables of z-score or a z-score calculator. You cannot derive the value analytically.The required z-score is 0.524401

What is the probability that an offspring will be black in the cross shown in punnett square B?

If you want to ask questions about something that is "shown", then I suggest that you make sure that there is something that is shown.

How many permutations are there for the letters in the word basketball?

BASKETBALL = 10 letters

B=2

A=2

S=1

K=1

E=1

T=1

L=2

Number of permutations = 10! /2!2!2!

= 10x9x8x7x6x5x4x3x2 / 2x2x2

=3,628,800 / 8

=453,600

What is the probability of not drawing a heart?

Number of cards in a deck = 52

Number of cards that are heart = 13

Therefore number of cards that are not heart = 52-13 = 39

Probability of not drawing a heart = 39/52 or 3/4

Can the probability be more than 1 or less than 0?

No, all probabilities are given from a scale of 0 to 1. 0 represents 0% and 1 represents a 100% probability.

What are equally likely event?

Two events that have the same chance of happening. For example, if I flip a coin the event of obtaining a 'head' is equally as likely as the event of obtaining a 'tail'.

But equally likely does not mean 0.5 probability. It's possible that it's equally likely that someone in Ontario, Canada will die from being stung by a wasp as from being electrocuted in their kitchen at home. Neither event is very likely but the two events could be equally likely.

What is the formula of probability in math?

There is no single formula for probability, since there are many different aspects to probability.

There is no single formula for probability, since there are many different aspects to probability.

There is no single formula for probability, since there are many different aspects to probability.

There is no single formula for probability, since there are many different aspects to probability.