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In this lesson, we will learn how to find and compare between experimental and theoretical probabilities.

Q1:

If a letter is randomly selected from the word βValenciaβ what is the probability that it is βEβ?

Q2:

For a single roll of a die, find the probability of getting an even number.

Q3:

The table shows the number of employees in each department of a company. If an employee is selected at random, what is the probability that they are part of the sales department?

Q4:

A bag contains white, red, and black balls. The probability of drawing a white ball at random is 1 1 2 0 and a red ball at random is 3 1 0 . How many red balls and how many black balls are in the bag?

Q5:

What is the expected number of tails when a fair coin is flipped 690 times?

Q6:

A bag contains an unknown number of balls. one-sixth of them are white, one-fifth of them are green, and the rest are blue. If a ball is drawn at random from the bag, what is the probability that it is blue?

Q7:

A bag contains 8 white balls and 4 red balls. If a ball is chosen at random from the bag, what is the probability that the ball is white?

Q8:

Suppose we roll a fair die twice and denote the sum of the results by π . Calculate the probability that 5 < π < 1 1 .

Q9:

Suppose π is a sample space consisting of 14 equally like outcomes. Given π΄ β π and π ( π΄ ) = 1 3 , find π ( π΄ ) .

Q10:

Elizabeth wants to compare theoretical and experimental probabilities. She decides to roll a die 12 times, 120 times, and 1β200 times and then compare the three distributions.

After 12 rolls, she got the following results:

After 120 rolls, she got the following results:

After 1β200 rolls, she got the following results:

Elizabeth knows that the theoretical probability of rolling a 3 is 1 6 = 0 . 1 6 7 , correct to three decimal places.

Using the experiment with 12 trials, calculate the experimental probability of rolling a 3.

Using the experiment with 120 trials, calculate the experimental probability of rolling a 3. Give your answer as a decimal to three decimal places.

Using the experiment with 1200 trials, calculate the experimental probability of rolling a 3. Give your answer as a decimal to three decimal places.

If Elizabeth were to continue rolling her dice and record 12β000 rolls, would you anticipate that the experimental probability for rolling a 3 would get closer to or further away from the theoretical probability?

Q11:

A bag contains 28 balls, 10 of which are white, 9 are red, and 9 are black. If a ball is drawn at random, what is the probability of the ball being red?

Q12:

If a digit from the number 375β753β363 is selected at random, what is the probability that it is even?

Q13:

Given that the set { 2 , 1 } is used to write a two-digit number which may have repeated digits, determine the probability that the product of the digits of the number formed is 2.

Q14:

Given that the set { 4 , 7 } is used to write a two-digit number which has no repeated digits, determine the probability that the number formed is odd.

Q15:

A bag contains 100 balls. There are 14 red balls, 49 blue balls, and the remaining balls are white. If a ball is taken from the bag at random, what is the probability that the ball is not white? Give your answer to three decimal places.

Q16:

If a single digit is selected at random from the number 224β839β287, what is the probability of the digit being even?

Q17:

The ratio of boys to girls at a school club is 4 βΆ 1 . If a student is chosen at random from the club, what is the probability that they are a girl?

Q18:

Given that the set { 1 , 5 , 8 } is used to write a two-digit number which has no repeated digits, determine the probability that the tens digit is an odd number.

Q19:

In a class of 50 students, 33 passed the mathematics test and 31 passed the language test. What is the probability that a randomly selected student failed the language test?

Q20:

A class of 36 students took a maths exam where the maximum mark was 50. If 16 students got less than 40 marks, what is the probability that a student got greater than or equal to 40 marks?

Q21:

A class has 18 boys and 9 girls. What is the probability that a randomly selected student is a girl?

Q22:

A bag contains 25 red balls, 30 blue balls, and an unknown number of yellow balls. Given that the probability of choosing a blue ball from the balls is 6 1 9 . Find the probability of choosing a red ball.

Q23:

There are 28 people in a meeting. The probability that a person chosen at random is a man is 1 2 . Calculate the number of women in the meeting.

Q24:

What is the probability of rolling a number divisible by 5 on a fair die?

Q25:

What is the probability of rolling an even number greater than 1 on a fair die?

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