Mathematics : Probability

The probability that a leap year will have 53 Friday or 53 Saturday, is

• $\frac{2}{7}$

• $\frac{3}{7}$

• $\frac{4}{7}$

• $\frac{1}{7}$

Ten coins are thrown simultaneously, the probability of getting atleast 7 heads is

• $\frac{63}{256}$

• $\frac{121}{172}$

• $\frac{113}{512}$

• $\frac{11}{64}$

If four digits are taken fromthe digits 1, 2, 3, 4, 5, 6, 7. The probability that the sum of digits is less than 12, is

• $\frac{3}{35}$

• $\frac{4}{35}$

• $\frac{2}{35}$

• $\frac{1}{35}$

The probability of happening exactly one of the two events A and B is

• $\mathrm{P}\left(\mathrm{A}\right) + \mathrm{P}\left(\mathrm{B}\right) - 2\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right)$

• $\mathrm{P}\left(\mathrm{A}\right) + \mathrm{P}\left(\mathrm{B}\right) - \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right)$

• P(A) - P(B)

• None of the above

In a throw of two dice, the probability of getting a sum of 7 or 11 is

• $\frac{2}{9}$

• $\frac{7}{9}$

• $\frac{5}{9}$

• None of these

The probability that at least one of the events A and B occurs is 0.7 and they occur simultaneously with probability 0.2. Then, $\mathrm{P}\left(\overline{\mathrm{A}}\right) + \mathrm{P}\left(\overline{\mathrm{B}}\right)$ is equal to

• 0.8

• 0.6

• 1.1

• 1.4

Seven weddings occur in a week. What is the probability that they happen on the same day?

• $\frac{1}{7}$

• $\frac{1}{7^4}$

• $\frac{1}{7^6}$

• None of these

Two small squares on a chess board are chosen at random. Probability that they have a common side is

• $\frac{1}{3}$

• $\frac{1}{9}$

• $\frac{1}{15}$

• $\frac{1}{18}$

A die is thrown 7 times. What is the chance that an odd numberturns up exactly 4 times ?

• $\frac{35}{128}$

• $\frac{37}{128}$

• $\frac{4}{7}$

• $\frac{43}{128}$

If the integer $\mathrm{\lambda } \mathrm{and} \mathrm{\mu }$ are chosen at random between 1 and 100, then the probability that a number of the form $7^{\mathrm{\lambda }} + 7^{\mathrm{\mu }}$ is divisible by 5 is

• 1/4

• 1/7

• 1/8

• 1/49