Probability practice · Easy

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

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

Let $n(A-B)=25+x, n(B-A)=2 x$ and $n(A \cap B)=2 x$. If $n(A)=2 n(B)$ then ' $x$ ' is

7 white balls and 3 black balls are placed in a row at random. The probability that no two black balls are adjacent is

If $A$ and $B$ are two events such that $P(A)=\frac{2}{5}$ and $P(A \cap B)=\frac{3}{20}$, then the conditional probability $P\left(A / A^{\prime} \cup B^{\prime}\right)$, where $A^{\prime}$ denotes the complement of $A$, is equal to

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is :

The probability that a candidate secures a seat in Engineering through “EAMCET” is $1/10.$ 7 candidates are selected at random from a centre. The probability that exactly two will get seats is

The probability that the 6th day of a randomly chosen month of a year is a Sunday, is

Six coins are tossed simultaneously. The probability of getting at least 4 heads is

A lottery sells $n^2$ tickets and declares $n$ prizes. If a man purchases $n$ tickets, the probability of his winning exactly one prize is

A lot consists of 102 good pencils, 6 with minor defects and 2 with major defects. A pencil is choosen at random. The probability that this pencil is not defective is

A five digits number is formed by writing the digits 1, 2, 3, 4, 5 in a random order without repetitions. Then the probability that the number is divisible by 4, is

If the probability that a person is not a swimmer is 0.3 , then the probability that out of 5 persons 4 are swimmers is

The probability that a company executive will travel by train is $\frac{2}{3}$ and that he will travel by plane is $\frac{1}{5}.$ The probability of his journey by train or plane is

If a dice is thrown twice, the probability of occurrence of 4 at least once, is

You are given a box with 20 cards in it. 10 of these cards have letter $I$ printed on them. The other ten have the letter ${T}$ printed on them. If you pick up 3 cards at random and keep them in same order, the probability of making the word $IIT$, is

If $A$ and $B$ are arbitrary events, then

If a dice is thrown twice, the probability of occurrence of 4 at least once is

If $A$ and $B$ are two independent events such that $P(\bar{A} \cap B)=2 / 15$ and $P(A \cap \bar{B})=1 / 6$, then $P(B)$, is

If $A$ and $B$ are two events such that $P\left( {A \cup B} \right) = \frac{5}{6},$ $P\left( {A \cap B} \right) = \frac{1}{3}$ and $P\left( {\bar B} \right) = \frac{1}{3},$ then the value of $P\left( A \right)$ is