Probability practice · Mixed difficulty

A manufacture 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

If $P(A)=\frac{2}{3}, P(B)=\frac{1}{2}$ and $P(A \cup B)=\frac{5}{6}$, then events $A$ and $B$ are

If $A$ and $B$ are two independent events such that $P\left( B \right) = \frac{2}{7},P\left( {A \cup {B^c}} \right) = 0.8$, then $P\left( A \right)$ is equal to

Probability of getting positive integral roots of the equation ${x^2} - n = 0$ for the integer $n,\;\,1 \le n \le 40$ is

In a test, an examines either guesses or copies or knows the answer to a multiple choice questions with four choices. The probability that he makes a guess is $\frac{1}{3}$ and the probability that he copies the answer is $\frac{1}{6}.$ The probability that his answer is correct given that he copies it is $\frac{1}{8}.$ The probability that his answer is correct, given that he guesses it is $\frac{1}{4}.$ The probability that they knew the answer to the questions given that he correctly answered is

If two dice are thrown together, then the probability that the sum of numbers appearing on them is 9, is

Two number $a, b$ are chosen from the set of integers $1,2,3, \ldots ., 39$, then probability that the equation $7 a-9 b=0$ is satisfied, is

The probability that a student is not a car driver is $1 / 5$. The probability that out of 5 students, exactly 4 are car drivers is

An unbiased die is rolled twice. Let $A$ denote the event that an even number appears on the first throw and $B$ denote the event that an odd number appears on the second throw. Then $A$ and $B$

A letter is known to have come either from LONDON or CLIFTON; on the postmark only the two consecutive letters $\mathrm{ON}$ are legible. The probability that it came from LONDON is

For two events $A$ and $B$, if $P(A)=P(A / B)=\frac{1}{4}$ and $P(B / A)=\frac{1}{2}$, then

Four numbers are multiplied together. Then the probability that the product will be divisible by 5 or 10, is

Seven balls are drawn simultaneously from a bag containing 5 white and 6 green balls. The probability of drawing 3 white and 4 green balls is

Let $A=\{1,3,5,7,9\}, B=\{2,4,6,8\}$, if a Cartesian product $A \times B$ is choosen at random, the probability of $a+b=9$ is

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colours, is

Six dice are thrown simultaneously. The probability that all of them show the different faces, is

A fair die is rolled. The probability that the first time 1 occurs at the even throw, is

If $x \in \left[ {0,5} \right],$ then what is the probability that ${x^2} - 3\;x + 2 \ge 0?$

An MBA applies for a job in two firms $X$ and $Y$. The probability of his being selected in firim ${X}$ is 0.7 and being rejected at ${Y}$ is 0.5 . The probability of at least one of his applications being rejected is 0.6 . The probability that he will be selected in one of the firms, is

When a certain biased die is rolled, a particular face occurs with probability $\frac{1}{6} - x$ and its opposite face occurs with probability $\frac{1}{6} + x$. All other faces occurs with probability $1/60.$ Note that opposite faces sum to $7$ in any die. If $0\, < x\, < \,\frac{1}{6},$ and the probability of obtaining total sum $= 7,$ when such a die is rolled twice is 13/96, then the value of $x$ is

A speaks truth in $60 \%$ of the cases and B in $90 \%$ of the cases. The percentage of cases they are likely to contradict each other in stating the same fact is

A coin is tossed 3 times. The probability of obtaining at least two heads is

A matrix is chosen at random from the set of all $2 \times 2$ matrices with elements 0 and 1 only. The probability that the value of the determinant of the matrix chosen is positive, is

$A$ speaks the truth in 70 percent cases and $B$ in 80 percent. The probability that they will contradict each other when describing a single event is

If four dice are thrown together. Probability that the sum of the number appearing on them is 13, is

In a lottery three were 90 tickets numbered 1 to 90. Five tickets were drawn at random. The probability that two of the tickets drawn numbers 15 and 89, is

The numbers $1,2,3, \ldots, n$ are arranged in a random order. Then, the probability that the digits $1,2,3, \ldots ,\,k(k < n)$ appears as neighbours in that order, is

A box $B_1$ contains 1 white ball, 3 red balls and 2 black balls. Another box $B_2$ contains 2 white balls, 3 red balls and 4 black balls. A third box $B_3$ contains 3 white balls, 4 red balls and 5 black balls. If 1 ball is drawn from each of the three boxes $B_1, B_2$ and $B_3$, the probability that all 3 drawn balls are of the same colour is

The probability of occurrence of a multiple of 2 on one dice and a multiple of 3 on the other dice if both are thrown together, is:

All the spades are taken out from a pack of cards. From these cards, cards are drawn one by one without replacement till the ace of spades comes. The probability that the ace comes in the 4 th draw, is