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In this lesson, we will learn how to find and interpret the probability of independent events.

Q1:

A bag contains 22 red balls and 9 green balls. One red ball is removed from the bag and then a ball is drawn at random. Find the probability that the drawn ball is red.

Q2:

In a sample space π , the probabilities are shown for the combinations of events π΄ and π΅ occurring. Are π΄ and π΅ independent events?

Q3:

If two dice are rolled, what is the probability that the sum is 4 or doubles are rolled?

Q4:

A bag contains 8 red balls, 7 green balls, 12 blue balls, 15 orange balls, and 7 yellow balls. If two balls are drawn consecutively, without replacement, what is the probability that the first ball is red and the second is blue?

Q5:

Q6:

A fair six-sided die with the numbers 1 to 6 is rolled, and a fair coin is flipped. What is the probability that the number obtained on the die is a factor of 12 and the coin lands with its heads side down?

Q7:

π΄ and π΅ are independent events, where π ( π΄ ) = 1 3 and π ( π΅ ) = 2 5 . What is the probability that events π΄ and π΅ both occur?

Q8:

In an experiment a coin is flipped and a die is rolled once. Event π΄ is the appearance of a head and a prime number. Event π΅ is the appearance of an even number. Find the probability of event π΄ or event π΅ occurring but not both.

Q9:

One letter is randomly selected from the word EVEN, and another is randomly selected from the word LETTER. What is the probability that both letters are vowels?

Q10:

A coin is flipped three consecutive times. What is the probability of only getting one head?

Q11:

A fair coin is flipped and a fair die is rolled. What is the probability of rolling an even number on the die?

Q12:

An experiment consists of flipping a coin and rolling a fair six sided die once. Determine the probability of event π΄ , the coin landing head side up and the dice landing with a prime number uppermost.

Q13:

A card is drawn at random from a pack of cards numbered from 1 to 25. What is the probability that the drawn card has a number which is a factor of 10 or is even?

Q14:

A bag contains 10 white marbles, 7 black marbles, and 3 red marbles. If a marble is selected at random, find the probability of selecting a black or a red marble.

Q15:

A bag contains 16 white balls and 14 red balls. Two balls are drawn consecutively without replacement. What is the probability that both balls are white?

Q16:

A bag contains 6 blue balls and 15 red balls. If two balls are drawn without replacement, what is the probability of getting one blue ball and one red ball?

Q17:

A deck contains eight cards which are numbered 5, 7, 8, 9, 9, 15, 19, and 20. What is the probability of selecting a card at random which has a prime number?

Q18:

If these two spinners are spun, what is the probability that the sum of the numbers the arrows land on is a multiple of 9?

Q19:

A bag contains coloured balls, 18 of which are red. The rest of the balls are black. Two red balls are removed from the bag, and then a ball is drawn at random. What is the probability that the ball drawn is black, given that there were 99 balls in the bag at the start?

Q20:

For two events π΄ and π΅ , when is it true that π ( π΄ ) β π ( π΅ ) = π ( π΄ β© π΅ ) ?

Q21:

A bag contains 32 balls. There 27 red balls, which are numbered from 1 to 27, and 5 white balls which are numbered from 28 to 32. If a ball is chosen at random from the bag, what is the probability that the ball is white or has an odd number?

Q22:

A bag contains 18 balls, 5 of which are white, 9 are red, and 4 are black. If a ball is drawn at random, what is the probability of the ball being white or red?

Q23:

The table shows the number of tyres, from a sample of 800, which needed to be replaced after a range of distances. Using the table, calculate the probability that a tyre will need to be replaced after covering more than 50 kilometres.

Q24:

In a sample of 55 people, 28 of them have brown hair and 22 of them have blue eyes. 5 of them have neither brown hair nor blue eyes. What is the probability that a random person from the sample has at least one of these features.

Q25:

A bag contains 5 red balls, 2 yellow balls, and 4 black balls. What is the probability that a ball selected at random is red or yellow?

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