Arihant Expert Team Solutions for Exercise 1: PRACTICE QUESTIONS for Phase I

Two persons A and B appear in an interview for two vacancies. If the probabilities of their selections are $\frac{1}{4}$ and $\frac{1}{6}$ respectively, then the probability that none of them is selected, is:
 

The probabilities of solving a problem by three students A, B and C are $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that the problem will be solved, is

Out of $13$ applicants for a job, there are $5$ women and $8$ men. It is desired to select $2$ persons for the job. The probability that atleast one of the selected persons will be a woman, is: 

Five coins are tossed at a time. Then, the probability of obtaining atleast one tail is:

An urn contains $6$ red, $4$ blue, $2$ green and $3$ yellow marbles. If two marbles are picked at random, what is the probability that both marbles are red?
 

An urn contains $6$ red, $4$ blue, $2$ green and $3$ yellow marbles. If three marbles are picked at random, what is the probability that two is blue and one is yellow?

An urn contains $6$ red, $4$ blue, $2$ green and $3$ yellow marbles, If four marbles are picked at random, what is the probability that atleast one is blue?

An urn contains $6$ red, $4$ blue, $2$ green and $3$ yellow marbles, If two marbles are picked at random, what is the probability that either both are green or both are yellow?