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Exercises for Question Type 6: Working with replacement - IB | RevisionDojo

Question 1

A bag contains 10 marbles, 3 of which are red. If you draw two marbles without replacement from the bag and the second marble is red, what is the probability that the first marble was also red?

[5]

Question 2

A bag contains 10 marbles, of which 3 are red and 7 are blue.

What is the probability of drawing exactly two red marbles in three draws without replacement from the bag?

[3]

Question 3

A bag contains 3 red and 7 green marbles. You draw a marble and do not replace it. What is the probability that you draw a red marble first and a green marble second?

[4]

Question 4

A bag contains 3 red and 7 green marbles. You draw a marble at random and then replace it before drawing again. What is the probability that the first marble drawn is red?

[2]

Question 5

A bag contains $3$ red marbles and $7$ blue marbles.

What is the probability of drawing at least one red marble in three draws with replacement from the bag?

[4]

Question 6

A bag contains 3 red and 7 green marbles. You draw a marble, replace it, and then draw a second marble. What is the probability that the first marble is red and the second marble is green?

[2]

Question 7

A bag contains 10 marbles, 3 of which are red.

If you draw two marbles with replacement from the bag and the second marble is red, what is the probability that the first marble was also red?

[3]

Question 8

A bag contains 3 red marbles and 7 green marbles.

What is the probability of drawing two red marbles followed by one green marble in three draws without replacement from the bag?

[3]

Question 9

A bag contains 3 red marbles and 7 green marbles.

What is the probability of drawing two red marbles followed by one green marble in three draws with replacement from the bag?

[3]

Question 10

A bag contains red and green marbles, where the probability of drawing a red marble is $\frac{3}{10}$ . In $n$ draws with replacement from the bag, derive a formula for the probability of drawing exactly $r$ red marbles.

[4]

Question 11

A bag contains 3 red marbles and 7 green marbles.

What is the probability of drawing a red marble, then a green marble, then a red marble in three draws with replacement from the bag?

[2]

Question 12

A bag contains 7 green marbles and 3 red marbles.

What is the probability of drawing two green marbles followed by one red marble in three draws without replacement from the bag?

[3]

Question 13

A bag contains 3 red marbles and 7 green marbles.

Find the probability of drawing at least one red marble in three draws without replacement from the bag.

[3]

Question 14

A bag contains 3 red marbles and 7 blue marbles.

What is the probability of drawing exactly two red marbles in three draws with replacement from the bag?

[3]

Question Type 6: Working with replacement Exercises