G Tewani Solutions for Chapter: Probability, Exercise 1: DPP

The probability that a dealer will sell at least $20$ $\mathrm{T}.\mathrm{V}.$ sets during a day is $0.45$, and the probability that he will sell less than $24$ $\mathrm{T}.\mathrm{V}.$ sets is $0.74$. The probability that he will sell $20, 21, 22$ or $23$ $\mathrm{T}.\mathrm{V}.$ sets during the day is

Consider the Cartesian plane $R^2$ and let $X$ denote the subset of points for which both the coordinates are integers. A coin of diameter $\frac{1}{2}$ unit is tossed randomly onto the plane. The probability $p$ that the coin covers a point of $X$ is

The probabilities of events $A\cap B, A, B$ and $A\cup B$, are respectively in arithmetic progression with second term equal to the common difference. Therefore, $A$ and $B$ are

$5$ players of equal strength play one each with each other. $P\left(A\right)=$probability that at least one player wins all matches he (they) play. $P\left(B\right)=$probability that at least one player loses all his (their) matches

If $A$ and $B$ are exhaustive events in a sample space such that probabilities of the events $A\cap B, A, B$ and $A\cup B$ are in $\mathrm{A}.\mathrm{P}.$ and if $P\left(A\right)=K$, where $0<K\le 1$, then

A boy has a collection of blue and green marbles. The number of blue marbles belong to the set $\{2, 3, 4, \dots ,13\}$. If two marbles are chosen simultaneously, and at random from his collection, then the probability that they have different colours is $\frac{1}{2}.$ Possible number of blue marbles is

A fair coin is tossed $n$ times. Let $x$ denote the number of times the head occurs. If $P(x=4), P(x=5)$ and $P(x=6)$ are in arithmetic progression, then the value of $n$ can be

If $A_1, A_2,\dots \dots , A_n$ be any events of the same sample space, then