NCERT Solutions for Chapter: Probability, Exercise 1: Exercise

Rehan has a set of $40$ cards numbered $1-40$ without repeating any number. Rehan wants to construct $△\mathrm{PQR}$ shown below by choosing the length of $\mathrm{PR}$, in $\mathrm{cm}$, from the set of the cards.

What is the probability that a card chosen at random makes $△\mathrm{PQR}$ an OBTUSE angled triangle with $\mathrm{Q}$ as obtuse angle?

Five different letters are put inside $5$ addressed envelopes by an illiterate servant. What is the probability that only $2$ letters are placed in the correct envelopes?

Farah and Sheena are playing a game with number tokens. Each of them has four number tokens, $2, 3, 4$ and $5$. A token is randomly picked by each of them from their stack simultaneously. If the sum of the numbers picked by each of them is a prime number, Farah wins the game and if it is a composite number, then Sheena wins the game.

Find the probability of each of them winning the game and state who has a higher probability of winning the game. Show your work.

Jenin has four $50$-rupee notes, seven $100$-rupee notes and two $2000$-rupee notes in her purse. She doesn't have any other denomination of currency with her. She goes for shopping and buys a skirt for Rs $799$. She takes out a note from her purse at random.

$\mathrm{i})$ Find the probability that the note will be sufficient to pay for the dress.

$\mathrm{ii})$ Find the probability that she will be able to give exactly Rs $799$ to the shopkeeper.

Show your work.

On a given day, an airplane is carrying $78$ meals, of which $39$ are vegetarian and the rest are non-vegetarian.

If the air hostess started distributing the meal and picked the first meal from the lot, what is the probability that it has a surprise gift?

Shown below are two spinners.

Select the points on the probability scale below that represents:

$\mathrm{i})$ the probability of spinner $1$ landing on black region.

$\mathrm{ii})$ the probability of spinner $2$ landing on white region.

At a fair, there is a game such that it has two bags. Bag $1$ has an equal number of red(R) and yellow(Y) cubes and bag $2$ has an equal number of red(R) and blue(B) cubes. Rohit has to pick a cube from each of the bags. If he picks up at least $1$ red cube, he gets a prize.

Find the probability of Rohit getting a prize. List all outcomes and show your work.

In a cards game, there are ten cards, $1$ to $10$. Two players, seated facing each other, randomly choose $5$ cards each. They arrange their cards in ascending order of the number on the card as shown below.

The difference between the corresponding cards is calculated such that the lower value is subtracted from the higher value.

In a random game, what is the probability that the sum of the differences is $24$?