 # Probability Problems

In this worksheet, students answer questions on simple probability. Key stage:  KS 4

Curriculum topic:  Probability

Curriculum subtopic:  Calculate the Probability of Independent and Dependent Combined Events

Difficulty level:   ### QUESTION 1 of 10 This is usually written as a fraction, but if the event is certain then the probability is 1 and, if the event is impossible, the probability is 0.

Example

Five counters numbered 1 to 5 are placed in a bag.  If one counter is drawn out at random, what is the probability that it will be a counter with an even number?

Answer

From the numbers 1, 2, 3, 4, 5 there are just 2 even numbers out of 5 numbers.

The probability of getting an even number is 2/5

Six counters numbered 2, 4, 5, 7, 8, 9 are placed in a bag.

If one counter is drawn at random, what is the probability that it will be:

(a) a factor of 35

(b) even?

## Column B

Factor of 35
1/2
Even
1/3

A standard six faced die is thrown.

What is the probability that it will land showing a:

(a) prime number

(b) even number

(c) square number

(d) cube number?

## Column B

Prime
1/3
Even
1/2
Square
1/6
Cube
1/2

In a class of 30 children, 10 have blonde hair, 6 have red hair and the rest are dark haired.

If I choose one child at random, what is the probability that they will have dark hair?

(Write your answer as a fraction in its lowest terms in the form a/b)

There are 45 sheep in a field.

40 are white and the rest are black.

If I select one sheep at random, what is the probability that it is black?

(Write your answer as a fraction in its lowest terms in the form a/b)

There are 45 sheep in a field.

Two thirds of them are white and the rest are black.

If I select one sheep at random, what is the probability that it is black?

(Write your answer as a fraction in its lowest terms in the form a/b)

The separate letters which make up the sentence

I LOVE MA THS

are placed in a bag.

I select one letter at random.

What is the probability that it will be a vowel?

(Write your answer as a fraction in its lowest terms in the form a/b)

The separate letters which make up the sentence

I LOVE MATHS

are placed in a bag.

I select one letter at random.

What is the probability that it will be the letter W?

The separate letters which make up the sentence

I LOVE MATHS MORE THAN ANYTHING ELSE

are placed in a bag.

I select one letter at random.

Which is more likely to be chosen, a vowel or a consonant?

Vowel

Consonant

There are 52 playing cards in a standard pack.

I select one card at random.

Which is more likely to be chosen, a red suit or a black suit?

Red

Black

Both the same

There are 52 playing cards in a standard pack.

I select one card at random.

What is the probability that it will be a picture card (Jack, Queen or King)

(Write your answer as a fraction in its lowest terms in the form a/b)

• Question 1

Six counters numbered 2, 4, 5, 7, 8, 9 are placed in a bag.

If one counter is drawn at random, what is the probability that it will be:

(a) a factor of 35

(b) even?

CORRECT ANSWER

## Column B

Factor of 35
1/3
Even
1/2
EDDIE SAYS
The counters numbered with factors of 35 are 7 and 5, which is one third of the total number of counters in the bag.
Half of the counters in the bag are numbered with even numbers, so the probability of drawing one of them is 1/2.
• Question 2

A standard six faced die is thrown.

What is the probability that it will land showing a:

(a) prime number

(b) even number

(c) square number

(d) cube number?

CORRECT ANSWER

## Column B

Prime
1/2
Even
1/2
Square
1/3
Cube
1/6
EDDIE SAYS
There are three prime numbers on the dice: 2, 3 and 5 - so the probability of it landing on a prime number is 1/2.
There are three even numbers on the dice so, again, the probability of it landing on an even number is also 1/2.
The are two square numbers on the dice: 1 and 4 (1 x 1 and 2 x 2), so the probability of it landing on one of these is 1/3.
Finally, the only cube number on the dice is 1 (1 x 1 x 1), so the probability of the dice landing on the cube number is 1/6.
• Question 3

In a class of 30 children, 10 have blonde hair, 6 have red hair and the rest are dark haired.

If I choose one child at random, what is the probability that they will have dark hair?

(Write your answer as a fraction in its lowest terms in the form a/b)

CORRECT ANSWER
7/15
EDDIE SAYS
To work out the answer, we must first work out how many children in the class have dark hair.
30 - 10 - 6 = 14, so we know that 14 children have dark hair.
This means that the probability of choosing a dark haired child is 14/30. When written in it's lowest form, this is 7/15.
• Question 4

There are 45 sheep in a field.

40 are white and the rest are black.

If I select one sheep at random, what is the probability that it is black?

(Write your answer as a fraction in its lowest terms in the form a/b)

CORRECT ANSWER
1/9
EDDIE SAYS
First we must work out how many sheep are black.
45 - 40 = 5, so we know that 5 sheep are black.
the probability of choosing a black sheep is, therefore, 5/45. Written in it's lowest form, this is 1/9.
• Question 5

There are 45 sheep in a field.

Two thirds of them are white and the rest are black.

If I select one sheep at random, what is the probability that it is black?

(Write your answer as a fraction in its lowest terms in the form a/b)

CORRECT ANSWER
1/3
EDDIE SAYS
First of all, we must work out how many sheep are black. To do this, we need to work out what a third of 45 is.
45 ÷ 3 = 15, so there are 15 black sheep in the field.
The probability of picking a black sheep is 15/45, which, when written in it's lowest form, is 1/3.
• Question 6

The separate letters which make up the sentence

I LOVE MA THS

are placed in a bag.

I select one letter at random.

What is the probability that it will be a vowel?

(Write your answer as a fraction in its lowest terms in the form a/b)

CORRECT ANSWER
2/5
EDDIE SAYS
There are 10 letters in total, four of which are vowels.
The probability of picking a vowel from the bag is 4/10. Written in its lowest form, this is 2/5.
• Question 7

The separate letters which make up the sentence

I LOVE MATHS

are placed in a bag.

I select one letter at random.

What is the probability that it will be the letter W?

CORRECT ANSWER
0
EDDIE SAYS
There is no W in the phrase 'I LOVE MATHS', which means that it is impossible for the letter to be picked from the bag. We write this probability as 0.
• Question 8

The separate letters which make up the sentence

I LOVE MATHS MORE THAN ANYTHING ELSE

are placed in a bag.

I select one letter at random.

Which is more likely to be chosen, a vowel or a consonant?

CORRECT ANSWER
Consonant
EDDIE SAYS
There are 11 vowels and 19 consonants in the bag. The probability of choosing a vowel is, therefore, 11/30, and the probability of choosing a consonant is 19/30. This means that you a more likely to choose a consonant than a vowel.
• Question 9

There are 52 playing cards in a standard pack.

I select one card at random.

Which is more likely to be chosen, a red suit or a black suit?

CORRECT ANSWER
Both the same
EDDIE SAYS
There are 52 cards in a standard pack; 26 red and 26 black. This means that the probability of choosing either is 26/52 and, therefore, both the same.
• Question 10

There are 52 playing cards in a standard pack.

I select one card at random.

What is the probability that it will be a picture card (Jack, Queen or King)

(Write your answer as a fraction in its lowest terms in the form a/b)

CORRECT ANSWER
3/13
EDDIE SAYS
There are 12 picture cards in a standard deck of cards. This means that the probability of picking one is 12/56. When written in its lowest form, this is 3/13.
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