Math Answers

solve system of linear differential equations  dx/dt-4y=1 and dy/dt+x=2

A secretary makes 2 errors per page on the average. What is the probability that on the next page she makes

a) 4 or more errors?

b) No errors?

The probability that a freshman entering AAU (Science Faculty) will survive first semester is 0.92. (From

1993/94 academic year statistics). Assuming this pattern remain unchanged over the subsequent years, what

is the probability that among 100 randomly selected freshmen in first semester,

a) None will survive?

b) Exactly 97 will survive?

c) At least three will survive?

Two dice are rolled. Let X be a random variable denoting the sum of the numbers

on the two dice.

i) Give the probability distribution of X

ii) Compute the expected value of X and its variance

Let A and B be two events associated with an experiment and suppose that P(A)=0.4 while P(AUB)=0.7. Let

P(B)=P

a) For what choice of P are A and B mutually exclusive?

b) For what choice of P are A and B independent?

In a large graduating class of 100 students 54 studied mathematics, 69 studied library science, and 35 studied

both mathematics and library science. If one of these students is selected at random, find the probability that

a) The student takes mathematics or library science

b) The student does not take either of these subjects

c) The student takes library science but not mathematics

In how many ways can a committee of three be chosen from 4 married couples if

a) All are equally eligible?

b) One particular man must be on the committee?

A stone is thrown vertically upward from the ground with an initial velocity of 40 ft/sec. 

 What is the height of the ball when its velocity is one-half the initial velocity?

Determine the half-life of the radioactive substance

A population consists of the numbers 1, 2, 3, and 4 with the sample size of 2 (without replacement). Which mean that has a probability of 2/6 or 1/3 or 0.33?