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.

A number was selected at random from $1 \mathrm{to} 100$ (inclusive of both numbers) and it was found to be a multiple of $10$.

What is the probability that the selected number is a multiple of $5?$

At a party, there is one last pizza slice and two people who want it. To decide who gets the last slice, two fair six-sided dice are rolled. If the largest number in the roll is:

• $1, 3 \mathrm{or} 6$, Ananya would get the last slice, and 
• $2, 4 \mathrm{or} 5$, Pranit would get it.

In a random roll of dice, who has a higher chance of getting the last pizza slice?

(Note: If the number on both the dice is same, then consider that number as the larger number.)

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 $24$?