1) What is the probability of flipping a coin twice and getting a head on both of the flips?

2) I roll a dice twice. What are the probabilities of the following outcomes occurring?

a) I roll two 3’s

b) I roll a 4 on the first roll and a 5 on the second roll

c) I roll two even numbers

d) I roll an even on the first roll and a 6 on the second roll

e) I roll a 2 on the first roll and a 7 on the second

f) I roll a number that is less than 3 on the first roll and a number that is greater than 5 on the second roll

g) I do not roll a 5 on the first roll and roll a 2 or a 3 on the second roll

3) I have a bag that contains 3 red balls and 2 blue balls. After I have picked a ball out of the bag, I place the ball back into the bag (there will always be 3 red balls and 2 blue balls when I pick a ball out of the bag).

I pick a ball from the bag twice. Work out the probabilities of the following events occurring:

a) Both of the balls are red

b) Both of the balls are blue

c) The first ball is red and the second is blue

d) The first ball is blue and the second is red

I pick a ball from the bag 3 times. Work out the probability of the following events occurring:

e) All 3 of the balls are red

f) I pick a red on the first pick, blue on the second pick and red on the final pick

g) I pick a blue on the first pick, another blue on the second pick and a red on the final pick

4) There are 6 chocolates in a box; 4 of the chocolates are fudge and 2 of the chocolates are caramel. I pick a chocolate at random and then eat it (thus meaning that the chocolate is not replaced). Work out the probabilities of the following outcomes:

a) Both of the chocolates that I pick are fudge

b) Both of the chocolates that I pick are caramel

c) I pick a fudge first and then pick a caramel

d) I pick a caramel and then a fudge

e) I pick a fudge and a caramel in any order

5) A fruit bowl contains apples, bananas and oranges. There are 5 apples, 2 bananas and 3 oranges. The fruit is not replaced after it has been taken out of the bowl. Find the probabilities of the following events occurring.

a) Picking an apple on the first pick and then a banana on the second

b) Picking an orange on both the first and second pick

c) Picking an apple or orange on the first pick and banana on the second

d) Picking an apple and an orange in any order

e) Picking 3 apples in a row

2) I roll a dice twice. What are the probabilities of the following outcomes occurring?

a) I roll two 3’s

b) I roll a 4 on the first roll and a 5 on the second roll

c) I roll two even numbers

d) I roll an even on the first roll and a 6 on the second roll

e) I roll a 2 on the first roll and a 7 on the second

f) I roll a number that is less than 3 on the first roll and a number that is greater than 5 on the second roll

g) I do not roll a 5 on the first roll and roll a 2 or a 3 on the second roll

3) I have a bag that contains 3 red balls and 2 blue balls. After I have picked a ball out of the bag, I place the ball back into the bag (there will always be 3 red balls and 2 blue balls when I pick a ball out of the bag).

I pick a ball from the bag twice. Work out the probabilities of the following events occurring:

a) Both of the balls are red

b) Both of the balls are blue

c) The first ball is red and the second is blue

d) The first ball is blue and the second is red

I pick a ball from the bag 3 times. Work out the probability of the following events occurring:

e) All 3 of the balls are red

f) I pick a red on the first pick, blue on the second pick and red on the final pick

g) I pick a blue on the first pick, another blue on the second pick and a red on the final pick

4) There are 6 chocolates in a box; 4 of the chocolates are fudge and 2 of the chocolates are caramel. I pick a chocolate at random and then eat it (thus meaning that the chocolate is not replaced). Work out the probabilities of the following outcomes:

a) Both of the chocolates that I pick are fudge

b) Both of the chocolates that I pick are caramel

c) I pick a fudge first and then pick a caramel

d) I pick a caramel and then a fudge

e) I pick a fudge and a caramel in any order

5) A fruit bowl contains apples, bananas and oranges. There are 5 apples, 2 bananas and 3 oranges. The fruit is not replaced after it has been taken out of the bowl. Find the probabilities of the following events occurring.

a) Picking an apple on the first pick and then a banana on the second

b) Picking an orange on both the first and second pick

c) Picking an apple or orange on the first pick and banana on the second

d) Picking an apple and an orange in any order

e) Picking 3 apples in a row