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Find the probability that Event A, drawing a spade on a single draw from a deck of cards, and Event B, rolling a total of 7 on a single roll of a pair of dice, will both occur.

A bowl contains eight chips. Three of the chips are red and the remaining five are blue. If two chips are drawn successively, at random and without replacement, what is the probability that the first chip drawn is red and the second dratwn is blue?

From an ordinary deck of playing cards, cards are drawn successively at random and without replacement. Compute the probability that the third spade appears on the sixth draw.

Columbia University has 2 major undergraduate divisions, Columbia College and Barnard College. Columbia College comprises \(60 \%\) of the undergraduate population and Barnard \(40 \%\). The percent of Columbia College students that commit suicide is \(2 \%\), while \(1 \%\) of the Barnard women take their own life. Taking one student at random, what is the probability that it is a (a) Columbia College student staying alive? (b) Barnard student remaining alive? (c) Columbia student about to commit suicide? (d) Barnard girl about to kill herself?

Four cards are to be dealt successively, at random and without replacement, from an ordinary deck of playing cards. Find the probability of receiving a spade, a heart, a diamond, and a club, in that order.

A bag contains 1 white ball and 2 red balls. A ball is drawn at random. If the ball is white then it is put back in the bag along with another white ball. If the ball is red then it is put back in the bag with two extra red balls. Find the probability that the second ball drawn is red. If the second ball drawn is red, what is the probability that the first ball drawn was red?

In the St. Petersburg Community College, \(30 \%\) of the men and \(20 \%\) of the women are studying mathematics. Further, \(45 \%\) of the students are women. If a student selected at random is studying mathematics, what is the probability that the student is a woman?

A box contains 4 black marbles, 3 red marbles, and 2 white marbles. What is the probability that a black marble, then a red marble, then a white marble is drawn without replacement?