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.

Shown below is a game with $3$ spinners attached to $3$ rooms. Each player is given a treasure which has to be kept in one of the rooms. All the spinners are rotated and if the spinner lands on the grey region, the room is opened. If the player kept his treasure in that room, he loses the treasure. If he kept in any other room, he wins the treasure.

Zaira kept her treasure in the room which is least likely to be opened.

In which room did she keep her treasure? show your work.

Shivesh was tossing a fair coin. Shown below are the outcomes of his first $5$ tosses.

Tail Tail Tail Tail Tail

Is the probability of Shivesh getting a head in his sixth toss higher than the probability of getting a tail? Give a valid reason.

Rohan has a bag of multiple balls either pink, green or yellow in colour. He randomely picks up one ball.

His friend, Farid predicted, "The probability of Rohan picking a pink ball is definitely $\frac{1}{3}$ as there are $3$ colours".

Is Farid's statement true or false. Give a valid reason or a counter example.

Shown below are two baskets with grey and black balls.

Abhishek is playing a game with his friend where he has to close his eyes and pick a black ball from one of the baskets in one trial.

He said "I will try with basket $2$ as it has a higher number of black balls than basket $1$ and hence the probability of picking a black ball from basket $2$ is higher."

Is Abhishek's statement correct? Justify your answer.

On a particular day, Vidhi and Unnati couldn't decide on who would get to drive the car. They had one coin each and flipped their coins exactly three times. The following was agreed upon:

• If Vidhi gets heads in a row, she would drive the car.
• If Unnati gets a head immediatley followed by a tail, she would drive the car.

Who has more probability to drive the car that day? List all outcomes and show your steps.

A $4$-sided fair die is numbered $1-4$. Nikhil and Pratik are playing with such a die each. They roll their dice once at the same time. A player wins only if they get a number larger than the other player.

What is the probability of Pratik winning the game? Show your work.

Shown below is a square dart board with circular rings inside.

Find the probability that a dart thrown at random lands on the shaded area. Show your steps.