Embibe Experts Solutions for Chapter: Probability, Exercise 1: COMEDK UGET 2014

An urn contains $9$ balls, $2$ of which are white, $3$ blue and $4$ black. $3$ balls are drawn at random from the urn. The chance that $2$ balls will be of the same colour and the third of a different colour is

$6$ boys and $6$ girls sit in a row at random. The probability that all the girls sit together is

Consider an experiment $E$ in which a box contains $10$ identical tickets numbered $1$ to $10$ and $2$ tickets are drawn at random from the box. What is the probability that both the tickets have even numbers on them?

Three dice are rolled once. The chance of getting a score of $5$ is

If the occurrence of an event $A$ implies the occurrence of an event $B$, then $P\left(A^c\cap B^c\right)$ is equal to

A bag contains $3$ white, $4$ black, $2$ red balls. If $2$ balls are drawn at random, then the probability that both the balls are white is

A card is picked at random from a pack of cards. Given that the picked card is a Queen, what is the probability that it is a spade?

A certain item is manufactured by $3$ factories $F_1,F_2$ and $F_3$ with $30\%$ of items made in $F_1,20\%$ in $F_2$ and $50\%$ in $F_3$. It is found that $2\%$ of the items produced by $F_1,3\%$ of the items produced by $F_2$ and $4\%$ of the items produced by $F_3$ are defective. Suppose that an item selected at random from the stock is found defective. What is the probability that the item came from $F_1$ ?