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

56.

If $\frac{1 + 4\mathrm{p}}{4}, \frac{1 - \mathrm{p}}{4}, \frac{1 - 2\mathrm{p}}{2}$ are the probabilities of three mutually exclusive events, then

• $\frac{1}{3} \le \mathrm{p} \le \frac{1}{2}$

• $\frac{1}{3} \le \mathrm{p} \le \frac{2}{3}$

• $\frac{1}{6} \le \mathrm{p} \le \frac{1}{2}$

• None of these

If A and B are two events, then $\mathrm{P}\left(\overline{\mathrm{A}} \cap \mathrm{B}\right)$ is equal to

• $\mathrm{P}\left(\overline{\mathrm{A}}\right)\mathrm{P}\left(\overline{\mathrm{B}}\right)$

• 1 - P(A) - P(B)

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

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

Two dice are thrown simultaneously. The probability of getting a pair of ACE is

• 1/36

• 1/3

• 1/6

• None of these

If two events A and B are mutually exclusive events, then P(A/B) is equal to

• 0

• 1

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

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

If A and B are two such events that $\mathrm{P}\left(\mathrm{A} \cup \mathrm{B}\right) = \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right)$, then which of the following is true?

• P(a) + P(B) = 0

• P(A) + P(B) = P(A)P(B/A)

• P(A) + P(B) = 2P(A)P(B/A)

• None of the above