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Probability

Multiple Choice Questions

31.

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

$\frac{1}{36}$
$\frac{3}{36}$
$\frac{11}{36}$
$\frac{20}{36}$

32.

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

33.

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

$\frac{2}{7}$
$\frac{2}{3}$
$\frac{3}{8}$
$\frac{1}{8}$

34.

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

$\frac{1}{190}$
$\frac{1}{120}$
$\frac{3}{190}$
$\frac{5}{190}$

35.

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')

36.

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

38.
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 ?

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{2}{5}$

$\frac{1}{3}$

Let A and B be two events such that

A = getting number 2 at least once

B = getting 7 as the sum of the numbers on two dice

We have,
A = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (1, 2), (3, 2), (4, 2), (5, 2), (6, 2)

and

B = {(2, 5), (5, 2), (6, 1), (1, 6), (3, 4), (4, 3)}

$∴ P (A) = \frac{11}{36}, P (B) = \frac{6}{36} P (A \cap B) = \frac{2}{36} Now, required probability P (A / B) = \frac{P (A \cap B)}{P (B)} = \frac{\frac{2}{36}}{\frac{6}{36}} = \frac{2}{6} = \frac{1}{3}$

39.

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