Maharashtra Board Solutions for Chapter: Probability, Exercise 1: EXERCISE 9.1

Two fair dice are thrown. State the sample space and write the favorable outcomes for the following event.

$D$: Even number on the first die.

Two fair dice are thrown. We have event

$A:$ Sum of numbers is divisible by $3$ or $4$

$B:$ Sum of numbers is $7$

Check whether events $A$ and $B$ are mutually exclusive and exhaustive. 

Two fair dice are thrown. State the sample space and write the favorable outcomes for the following two events $C$ and $D$. Also, check whether events are mutually exclusive and exhaustive. 

$C:$  an event that odd number occurs on first die

$D:$ an event that number on first die is an even number

A bag contains four cards marked as $5$, $6$, $7$ and $8$. Find the sample space if two cards are drawn at random with replacement. 

A bag contains four cards marked as $5$, $6$, $7$ and $8$. Find the sample space if two cards are drawn at random without replacement. 

From a bag containing $10$ red, $4$ blue and $6$ black balls, a ball is drawn at random. Find the probability of drawing a blue or black ball.

Find the probability of getting both red balls, when from a bag containing $5$ red and $4$ black balls, two balls are drawn without replacement.

A room has three sockets for lamps. From a collection $10$ bulbs, $6$ are defective. At night a person selects $3$ bulbs, at random and puts them in sockets. What is the probability that the room is lit.