Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is

• $\frac{1}{36}$

• $\frac{3}{36}$

• $\frac{11}{36}$

• $\frac{20}{36}$

The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A') + P(B') is

• 0.9

• 0.15

• 1.1

• 1.2

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')

One ticket is selected at random from 100 tickets numbered 00, 01, 02,..., 98, 99. If x₁ and x₂ denote the sum and product of the digits on the tickets, then P(x₁ = 9/x₂ = 0) is equal to

• $\frac{1}{50}$

• $\frac{2}{19}$

• $\frac{19}{100}$

• None of these

37.

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

• $\frac{1}{5}$

• $\frac{1}{10}$

• $\frac{3}{20}$

• $\frac{1}{20}$