Embibe Experts Solutions for Exercise 9: Assignment

From the set $S=\left\{0,1,2,\dots ,53\right\}$, three distinct numbers are chosen. The probability that the sum of them is $54$ is

A fair coin is tossed three times. Consider the events
$A=${First toss is head}

$B=${Second toss is head}

$C=${Exactly two heads in a row}

Which of the following statements is true?

If $A$ and $B$ are two events such that $P\left(A\right)=\frac{1}{2}$ and $P\left(B\right)=\frac{1}{3}$ then which of following is/are true?

There are $3$ men, $2$ women and $4$ children. If $4$ persons are selected then which of the following is/are true?

If the letters of word ASSASSIN are written at random in a row, then which of following are true?

If alphabets of word RAKESH are written in given boxes, then probability that no row remains empty is

If $A,B,C$ are events such that $P\left(A\right)=0.3$, $P\left(B\right)=0.4, P\left(C\right)=0.8, P\left(A\cap B\right)=0.08, P\left(A\cap C\right)=0.28,$$P\left(A\cap B\cap C\right)=0.09$. If $P\left(A\cup B\cup C\right)\ge 0.75$ then $P\left(B\cap C\right)$ can be

If three squares of dimension $1\times 1$ are selected at random from the chess board, then the probability that they form the letter $L$ is