Probability

A and B are two independent events such that P(A $\cup$ B') = 0.8, and P(A) = 0.3. Then, P(B) is

• $\frac{2}{7}$

• $\frac{2}{3}$

• $\frac{3}{8}$

• $\frac{1}{8}$

Three numbers are chosen at random from 1 to 20. The probability that they are consecutive is

• $\frac{1}{190}$

• $\frac{1}{120}$

• $\frac{3}{190}$

• $\frac{5}{190}$

Let E' denote the complement of an event E. Let E, F, G be pairwise independent events such that P(G) > 0 and P(E ∩ F ∩ G) = 0. Then, P(E' $\cap$ F' /G) equals

• P(E') + P(F')

• P(E') - P(F')

• P(E') - P(F)

• P(E) - P(F')

A four-digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd, is

• zero

• $\frac{1}{3}$

• $\frac{1}{4}$

• None of these

A die is rolled twice and the sum of the numbers appearing on them is observed to be 7. What is the conditional probability that the number 2 has appered atleast once ?

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{2}{3}$

• $\frac{2}{5}$

A manufacturer of cotter pins knows that 5% of his product is defective. He sells pins in boxes of 100 and guarantees that not more than one pin will be defective in a box. In order to find the probability that a box will fail to meet the guaranteed quality, the probability distribution one has to employ is

• binomial

• poisson

• normal

• exponential

Probability of getting positive integral roots of the equation x - n = 0 for the integer n, $1 \le \mathrm{n} \le 40$ is

• $\frac{1}{5}$

• $\frac{1}{10}$

• $\frac{3}{20}$

• $\frac{1}{20}$

A box contains 9 tickets numbered 1 to 9 inclusive. If 3 tickets are drawn from the box one at a time, the probability that they are alternatively either {odd, even, odd} or {even, odd, even}is:

• $\frac{5}{17}$

• $\frac{4}{17}$

• $\frac{5}{16}$

• $\frac{5}{18}$

If $\mathrm{P}\left(\mathrm{A}\right) = \frac{1}{12}, \mathrm{P}\left(\mathrm{B}\right) = \frac{5}{12} \mathrm{and} \mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}}\right) = \frac{1}{15}$, then P(A $\cup$ B) is equal to :

• $\frac{89}{180}$

• $\frac{90}{180}$

• $\frac{91}{180}$

• $\frac{92}{180}$

A bag contains 3 black and 4 white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn ball is white, is

• $\frac{4}{49}$

• $\frac{1}{7}$

• $\frac{4}{7}$

• $\frac{12}{49}$