Probability

if we assume that the probability for a girl being born is the same as a boy being born: (1/2)^6 = 0.015625 = 1.5625%

there is 0% probability, unless you are some super nerd, and calculate the chance of it splitting the six and you getting two threes in one roll :p

There are 12 face cards in a standard deck of 52 cards. The odds of the first card being a face card is 12/52. If the first card drawn is a face card then there are 11 face cards remaining in the deck of 51 cards. The odds of a second draw of a face card is then 11/51. If both the first two cards drawn were face cards then the deck has 10 face cards in 50 total card. The odds of the third card also being a face card is 10/50. The total probability is (12/52)*(11/51)*(10/50) = 0.009954751 or just under one percent of the time.

P(H and H and H and H)= 1/2 X 1/2 X 1/2 X 1/2 = 1/16

what game are you referring to?

The probability is always a fraction except when it is 0 or 1. If a probability = 1 then it will definitely happen. If the probability is 0 then it will not happen. If you toss a fair coin the probability of heads is 1/2, and the probability of tails is 1/2. These fractions are representations of the probabilities. Not all fractions are representative of probabilities. Fractions can be used to represent a portion of a whole. Like what portion of a class is boys, and what portion is girls: If there are 8 boys and 7 girls, then the 8/15 of the class is boys, and 7/15 of the class is girls.

The experimental probability of a number cube that lands on 5 four times in a twenty

toss trial is Pexp(5) = 4/20 = 1/5 = 0.20 = 20%

Ok, sounds like a trick question. Obviously, there can be only one result, either heads or tails. Generally, when we consider the set of possible outcomes, we would say a coin flip has 2: a head and a tail. If I really want to complicate the matter, I could include that the coin might land on an edge. Don't think its realistic to include landing on an edge as an outcome. Ok, sounds like a trick question. Obviously, there can be only one result, either heads or tails. Generally, when we consider the set of possible outcomes, we would say a coin flip has 2: a head and a tail. If I really want to complicate the matter, I could include that the coin might land on an edge. Don't think its realistic to include landing on an edge as an outcome.

If there are 12 boys and 6 girls, the total number of students would be 18.

You are looking for the probability of selecting a girl from the class:

6/18

Just reduce the fraction to its lowest form

6/18 = 2/6 = 1/3

Your answer would be 1/3.

Assuming that the probability of having a baby girl is 1/2 and that of having a baby boy is 1/2, the probability of having 3 baby girls in a row is (1/2)(1/2)(1/2)=1/8.

This question is extremely poorly phrased.

The probability of three boys [sitting] in a row at an all boys school is 1. At an all girls school it is 0 and is otherwise somewhere in between.

If the question is about birth order, do you take account of the fact that nearly half the families have two or fewer children? So that in half the cases the probability is 0.

Finally, children's genders are not independent events. They depend on the parents' ages and their genes.

However, if you assume that they are independent events then, given that the probability of a boy is approx 0.52, the probability of giving birth to three boys in a row is 0.523 = 0.1381

The probability that a trainee will remain with a company is 0.6. The probability that an employee earns more than Rs.10, 000 per year is 0.5. The probability that an employee is a trainee who remained with the company or who earns more than Rs.10, 000 per year is 0.7. What is the probability that an employee earns more than Rs.10, 000 per year given that he is a trainee who stayed with the company.

The odds against student X solving a Business statistics problem are 8 to 6, and odds in favour of student Y solving the problem are 14 to 16.

What is the chance that the problem will be solved if they both try independent of each other?

What is the probability that none of them is able to solve the problem?

Question 2: Marks: 1+3+2+3+1= 10

For the frequency distribution given below:

Length of Service No of employees

7.5-7.9 6

8.0-8.4 22

8.5-8.9 36

9.0-9.4 18

9.5-9.9 14

10.0-10.4 4

Calculate

Mean

Standard deviation

Co-efficient of Variation

Mean Deviation (from median)

Range

Question 3: Marks: 2+2=4

How many distinct four-digit numbers can be performed from the following integers 1, 2, 3,4,5,6 if each integer is used only once?

What would be the shape and name of the frequency distribution if

mean=median=mode

mean>median>mode

Question 4: Marks: 2+6=8

a) Describe the situation in which two variables are perfect positively correlated?

b) The cost of output at a factory is thought to depend on the number of units produced. Data have been collected for the number of units produced each month in the last six months, and the associated costs, as follows;

Output

('000s of units) X Cost

($'000) Y

2 9

3 11

1 7

4 13

3 11

5 15

Calculate the correlation coefficient and comment on your result.

Attempting Methodology / Requirements of the Assignment

This assignment covers Lesson No 9 to Lesson No 20

In Short answer question you can express your answer in 4-10 lines.

Illustrating your point you can give short examples

In numerical question, proper notation and symbols must be well written. For this use MathType Software.

Solve numerical step-by-step, giving all necessary explanation, whenever necessary.

1/6

If the probability of an event occurring is p, then 1-p represents the probability of the same event not occurring. The value of p must lie between 0 and 1.

1/16

* * * * *

The correct answer, however, is 4/16 = 1/4.

17 out of 21

z=(x-mean)/(standard deviation of population distribution/square root of sample size)

T-score is for when you don't have pop. standard deviation and must use sample s.d. as a substitute.

t=(x-mean)/(standard deviation of sampling distribution/square root of sample size)

If you rolled 2 fair dice, the probability of having a sum of 6 is 5 over 36

625

If digits can be reused, then 5x5x5x5x5 = 3125.

If digits cannot be reused, then 5x4x3x2x1 = 120.

Probabilities are calculated or estimated in a variety of methods. A non-quantitative means, used by weather forecasters, is to look at general conditions, is provide probabilies based on all indicators. In this way, the probabilities reflect their belief of certain events occurring from 0 (will not occur) to 100% (certain to occur). A second wasy probabilities are determined is to collect data, and determine the relative frequency of a particular event. Perhaps 10% of all motorists drive above the speed limit in a particular area, based on data collection, so we can state the probability of a motorist speeding in a certain area is 10%. Finally, probabilities are developed based on other known probabilites or assuming equally likely outcomes. If I have 5 outcomes, and they are equally likely, then the probability of each one occurring in 20% if these outcomes are independent and mutually exclusive. If I know the chance of coin flip coming up heads is 0.50, I can determine the probability of two coins coming up heads is 0.5 x 0.5 = 0.25.

Probability of picking purple sock first time is 6/10 or 3/5, second time, probability is 5/9.

Thus 3/5 * 5/9 = 15/45 which cancels to 1/3

7/10 X 6/9 = 42/90 it can be reduced to 7/15

polynomial functions: x2,x3,x1/2,x-1,xn if n doesn't equal 1 or 0

any trigonometric function: sin(x), cos(x), tan(x), sec(x), csc(x), cot(x)

exponential functions: 2x,3x,.5x,ex,nx if n doesn't equal 1 or 0.

any logarithmic function: log10(x), log2(x), ln(x), logn(x), for every n.

any inverse trig function: sin-1(x),sin-1(x),cos-1(x),tan-1(x),sec-1(x),csc-1(x),cot-1(x)

hyperbolic functions and their inverses: sinh(x),cosh(x),tanh(x),sech(x),csch(x),coth(x),

sinh-1(x),cosh-1(x),tanh-1(x),sech-1(x),csch-1(x),coth-1(x)

Hypergeometric function, Logarithmic integrals, Error functions, Fresnel integrals, Elliptic Integrals, and the integrals of nearly every other function.

Also, any combination of the above functions.