If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability 1/2.)

In answering a question on a multiple choice test,a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and 1/4 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/4. What is the probability that the studdent knows the answer given that he answered it correctly?

Let S be the set of all 2 x 2 symmetric matrices whose entries are either zero or one. A matrix X is chosen from S. The probability that the determinant of X is not zero is a) 1/3 b)1/2 c)3/4 d)1/4

What is the probability that a nümber selected from the numbers 1,2,3...... 25 is a prime number, when each of the given numbers is equally likely to be selected?

From all two-digit numbers with either digit 1, 2, or 3 one number is chosen i) What is the probability of both digits being the same? ii) What is the probability of the sum of the digits being 4 ?

There are 30 scouts and 20 guides in a school In another school, there are 20 scouts and 15 guides From each school, one student among them is to be selected for participation in a seminar a) What is the total number of possible selections? b) What is the probability of both being Scouts? c) What is the probability of both being guides? d) What is the probability of one scout and one guide?

In a third order determinant, each element of first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has the value a)1 b)9 c)16 d)24

Assume that each born child is equally likely to be a boy or a girl. If a family has two children,what is the conditional probability that both are girls given that the youngest is a girl