Probability

Q. Two squares are chosen at random on a chessboard, the probability that they have a side in common is:

1. $\frac{1}{18}$
2. $noneofthese$
3. $\frac{3}{32}$
4. $\frac{1}{32}$

Q. Seven digits from the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 are written in random order. The probability that this seven digit number is divisible by 9 is:

1. $\frac{7}{9}$
2. $\frac{1}{9}$
3. $\frac{2}{9!}$
4. $\frac{4}{9}$

Q. A four digit number is formed with the digits 1, 3, 4, 5 without repetition. Find the chance that the number is divisible by 5:

1. $\frac{3}{4}$
2. $\frac{1}{4}$
3. $\frac{9}{16}$
4. $\frac{1}{16}$

Q. From a group of 3 men and 2 women, two persons are selected at random. Find the probability that atleast one woman is selected.

1. $\frac{1}{5}$
2. $\frac{7}{10}$
3. $\frac{2}{5}$
4. $\frac{5}{6}$

Q. Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral equals:

1. $\frac{1}{3}$
2. $\frac{1}{10}$
3. $\frac{1}{6}$
4. $noneofthese$

Q. Two numbers b and c are chosen at random with replacement from the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9. The probability that $x^2+bx+c>0$ for all $xϵR$ is:

1. $\frac{23}{81}$
2. $\frac{7}{9}$
3. $\frac{32}{81}$
4. $\frac{65}{729}$

Q. A letter is taken out at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letters is:

1. $\frac{35}{96}$
2. $\frac{19}{90}$
3. $\frac{19}{96}$
4. $noneofthese$

Q. Four numbers are multiplied together. Then the probability that the product will be divisible by 5 or 10 is:

1. $\frac{169}{625}$
2. $\frac{369}{625}$
3. $\frac{169}{1626}$
4. $noneofthese$

Q. Nine squares are chosen at random on a chessboard. What is the probability that they form a square of size 3 $\times$ 3?

1. $\frac{9}{{}^{64}{C}_9}$
2. $\frac{6}{{}^{64}{C}_9}$
3. $noneofthese$
4. $\frac{36}{{}^{64}{C}_9}$

Q. The digits 1, 2, 3, 4, 5, 6, 7, 8, 9 are written in random order to form a nine digit number. Find the probability that this number is divisible by 4:

1. $\frac{4}{9}$
2. $\frac{2}{9}$
3. $\frac{17}{81}$
4. $noneofthese$