Embibe Experts Solutions for Chapter: Probability, Exercise 1: AP EAPCET - 20 Aug 2021 Afternoon

A coin is tossed $2020$ times. The probability of getting head on ${1947}^{\text{th }}$ toss is

If $A, B$ are two events with $P(A\cap B)=\frac{1}{3},P(A\cup B)=\frac{5}{6}$ and $P\left(A^C\right)=\frac{1}{2}$, then the value of $P\left(B^C\right)$ is

Let $X$ be a random variable which takes values $1,2,3,4$ such that $P(X=r)=K{r}^3$ where $r=1,2,3,4$ then

$P$ speaks truth in $70\%$ of the cases and $Q$ in $80\%$ of the cases. In what percent of cases are they likely to agree in stating the same fact

Box-I contains $3$ cards bearing numbers $1,2,3$; Box II contains $5$ cards bearing numbers $1,2,3,4,5$ and Box III contains $7$ cards bearing numbers $1,2,3,4,5,6,7$. One card is drawn at random from each of the boxes. If $x_i$ be the number on the card drawn from the ${\mathrm{i}}^{\mathrm{th} }$ box, $i=1,2,3$ then the probability that $x_1+x_2+x_3$ is odd is equal to

Tom and Jerry play a game of alternately throwing an unfair coin. First one to get head wins. If Tom starts the game, he has $62.5\%$ chance of winning the game. Suppose this coin is tossed $5$ times, then the probability of getting exactly $3$ heads is

A discrete random variable $X$ takes values $10,20,30$ and $40$, with probability $0.3,0.3,0.2,0.2$ respectively. Then the expected value of $X$ is

The range of a random variable $X$ is $\{1,2,3\dots ...\}$ and $P(X=x)=\frac{c^x}{x!}$, for $x=1,2,3,\dots \dots$ Then the value of $C$ is