Embibe Experts Solutions for Chapter: Probability, Exercise 4: Exercise-4

Find the chance of throwing $10$ exactly in one throw with $3$ dice.

Two players of equal skill, $A$ and $B$ are playing a set of games. They leave off playing when $A$ wants $3$ points and $B$ wants $2.$ If the share is Rs.$16$, what share each ought to take?

A family has three children. Event $\text{'}A\text{'}$ is that family has at most one boy, Event $\text{'}B\text{'}$ is that family has at least one boy and one girl, Event $\text{'}C\text{'}$ is that the family has at most one girl. Find whether events $\text{'}A\text{'}$ and $\text{'}B\text{'}$ are independent. Also find whether $A, B, C$ are independent or not.

A line segment of length $a$ is divided into two parts at random by taking a point on it, find the probability that no part is greater than $b,$ where $2b>a$

Two ants are on the opposite corners of a grid of size $8\times 8$ if they move then what is the probability that they will meet after each travelled eight steps (Assuming that they do not move in a backward direction)

If $r_1, r_2, r_3, r_4$ are four numbers which belong to the set $\{1,2,3,4,5,6,7,8\}.$ If $y=i^{r_1}+i^{r_2}+i^{r_3}+i^{r_4}$, where $i=\sqrt{-1}$. Find the probability of getting $y=4$.

If $r_1, r_2, r_3, r_4$ are four numbers which belong to the set $\{1,2,3,4,5,6,7,8\}$. If $y=i^{r_1}+i^{r_2}+i^{r_3}+i_4^{r_4},$ where $i=\sqrt{-1}$, probability of getting $y=-4$.

If $r_1, r_2, r_3, r_4$ are four numbers which belongs to the set $\{1, 2, 3, 4, 5, 6, 7, 8\}.$ If $y=i^{r_1}+i^{r_2}+i^{r_3}+i^{r_4},$ where $i=\sqrt{-1}$. Find the probability of getting $y=0$.