Mathematics : Probability

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

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

• $\frac{4}{49}$

• $\frac{1}{7}$

• $\frac{4}{7}$

• $\frac{12}{49}$

A coin is tossed 4 times. The probability that atleast one head turns up 1s

• $\frac{1}{16}$

• $\frac{2}{16}$

• $\frac{14}{16}$

• $\frac{15}{16}$

A speaks truth in 75% cases and B speaks truth in 80% cases, The probability that they contradict each other in a statement, is

• $\frac{7}{20}$

• $\frac{13}{20}$

• $\frac{3}{5}$

• $\frac{2}{5}$