Suppose that a person selects a card at random from a deck of 52 cards and tells us that the selected card is red. Find the probability that the card is the kind of hearts given that it is red.

Find the equation of the plane passing through (2,3, −1) and perpendicular to the line joining the points (3, 4, −1) and (2, −1, 5) .

The following data were obtained in a study of the relationship between the resistance (ohms) and the failure time (minutes) of certain overloaded resistors.

Four groups of students were subjected to different teaching techniques and tested at the end of a specified period of time. As a result of dropouts from the experimental groups the number of students varied from group to group. Do the data shown below present sufficient

evidence to indicate a difference in the mean achievement for the four teaching techniques at 0.01 level of significance? What is the conclusion if you fix the level of significance at 0.05?

Verify that f (x) = x/8 can serve as the probability density function of a continuous random variable which can take on any value in the interval from 0 to 4.

Vectors a and b are given by a = 3i − 2j + k and b = −2i + 2j + 4k . Find
i) magniture of a and b and the angle between them.
ii) projection of the vector (a +1/ 2b) onto a .
iii) which of the following vectors are perpendicular to a ?
c = −i − 4j + 2k, d = −3i + k, e = 2i + 2j − 2k .