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Theoretical Probability
A.T.4/
1.
There are 16 girls in a class of 24. A pupils is selected at random. What is the
probability that the selected pupil is :
(a) a girl,
2.
(b) A boy ?
A box contains 12 chocolates with soft centres and 18 chocolates with hard
centres.
(a) How many chocolates are there in the box ?
(b) Ellen chooses a chocolate at random from the box. What is the probability
that it has a hard centre ?
3.
Peter has a bag containing 30 pieces of lego.
Eight are coloured red, ten are coloured yellow and the rest are black.
Peter's friend Jim draws out a piece of lego from the bag.
What is the probability that the piece of lego drawn out by Jim is :
(a) red,
(b) black,
(c) white ?
4.
Three of the six apples in a fruit bowl are bad. Ray takes one of the apples.
What is the probability that it is a good one ?
5.
Rita chooses a month at random from the 12 months of the year.
What is the probability that the chosen month
(a) is the month of May ?
(b) begins with the letter J ?
(c) begins with vowel ?
6.
A day is chosen from the month of June.
What is the probability that the date of this day
(a) is even,
(b) will divide exactly by 10,
(c) will divide exactly by 5 ?
7.
One letter is chosen at random from the letters in the word 'SCHOOL'.
What is the probability that it is the letter 'O' ?
8.
Ishma writes down all the whole numbers from 1 to 10. She asks Kathryn to
choose one of these numbers. What is the probability that Kathryn chooses a
prime number ?
9.
The pupils of form 9AB are raffling an iced cake to raise money for Christmas
decorations. They sell 250 tickets at 5p each. Ying bought six tickets.
(a) How much money did form 9AB raise ?
(b) What is the probability that Ying wins the cake ?
10.
In a class there are 12 girls and 16 boys. One person is selected at random.
What is the probability that the selected person is
(a) a girl,
(b) a boy ?
(c) What is the total number if boys and girls ?
Check that you have used this total in your answer to questions (a) and (b).
11.
A number is chosen from the first 12 whole numbers.
What is the probability that the chosen number is
(a)
(b)
(c)
(d)
(e)
12.
less than ten,
A two-digit number,
exactly divisible by three,
an even number,
a multiple of 4 ?
One letter is chosen at random from the letters in the word 'TELEVISIONS".
What is the probability that it is
(a) a vowel,
13.
(b) a consonant,
A bag contains 6 red, 3 green and 15 black marbles.
What is the probability of choosing
(a) a red marble,
14.
(c) an 'E' ?
(b) a black marble
(c) a yellow marble ?
Suppose you have a set of 52 playing cards.
What is the probability of getting
(a)
(b)
(c)
(d)
the ten of spades,
an ace,
a picture card,
a diamond ?
A bag contains 3 yellow and 7 pink balls.
i) What is the probability of picking a pink ball ?
ii) If the ball you pick is pink and not put back, what is
the probability of picking another pink ball ?
iii) If a pink ball is picked and not put back, what is
the probability of picking a yellow ball ?
Answers
16 2

24 3
1)
a)
2)
a ) 30
3)
a)
4)
1
2
8 4

30 15
1
a)
12
15 1
a) 
30 2
2 1

6 3
4 2

10 5
5)
6)
7)
8)
8 1

24 3
18 3
b) 
30 5
12 6
b) 
30 15
b)
3 1

12 4
3 1
b) 
30 10
b)
6
250
12 3
16 4
a) 
b) 
28 7
28 7
9 3
3
a) 
b)
12 4
12
6 1
3 1
d) 
e) 
12 2
12 4
5
6
2
a)
b)
c)
11
11
11
9)
a ) 12.50
10 )
11 )
12 )
c )0
3 1

12 4
6 1
c) 
30 5
c)
b)
c ) 28
c)
4 1

12 3
6
1
15

b)
c) 0
24 4
24
1
4
1
12
6
3
a)
b)

c)


52
52 13
52 26 13
13 )
a)
14 )
Think about it
i)
7
10
ii)
6
9
iii)
3
9
d)
13
52