The Oakwood Academy
Probability (P1- 7)
(Expected outcomes; Relative frequency; Venn and
Tree Diagrams)
Page 1
The Oakwood Academy
Q1.
Two bags, A and B, contain numbered counters.
A counter is chosen at random from each bag.
Here are the 8 counters in bag A.
The table gives the probabilities of the numbers on the counters in bag B.
Number on counter
Probability
6
7
8
9
0.2
0.1
0.4
0.3
Which bag has the greater probability of choosing an even number?
You must show your working.
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Answer ......................................................................
(Total 2 marks)
Page 2
The Oakwood Academy
Q2.Samples are taken from a production line.
500 items are checked in each sample.
The relative frequencies of the number of faulty items in 5 samples are shown.
Sample
A
B
C
D
E
Relative frequency
0.032
0.04
0.026
0.016
0.028
Work out the range of the number of faulty items in the 5 samples.
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Answer ......................................................................
(Total 3 marks)
Page 3
The Oakwood Academy
Q3.
On Friday, Greg takes part in a long jump competition.
He has to jump at least 7.5 metres to qualify for the final on Saturday.
•
•
He has up to three jumps to qualify.
If he jumps at least 7.5 metres he does not jump again on Friday.
Each time Greg jumps, the probability he jumps at least 7.5 metres is 0.8
Assume each jump is independent.
(a)
Complete the tree diagram.
(2)
(b)
Work out the probability that he does not need the third jump to qualify.
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Answer ............................................
(2)
(Total 4 marks)
Page 4
The Oakwood Academy
Q4.A and B are independent events.
Fill in all eight missing probabilities in the diagram below.
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(Total 4 marks)
Page 5
The Oakwood Academy
Q5.
(a)
Shade the Venn diagram to show the region
(A ⋃ B)′
(1)
(b)
Shade the Venn diagram to show the region
A ⋂ B′
(1)
(Total 2 marks)
Page 6
The Oakwood Academy
M1.
0.2 + 0.4 or 0.6 oe (for bag B)
or
0.625 or 62.5(%) (for bag A)
M1
0.62(5) or 0.63 and 0.6 and bag A
oe
both probabilities correct in the same format and bag A
A1
[2]
M2.0.032 × 500 or A = 16 or
0.04 × 500 or B = 20 or
0.026 × 500 or C = 13 or
0.016 × 500 or D = 8 or
0.028 × 500 or E = 14
M1
0.04 × 500 or 20
and
0.016 × 500 or 8
Selects the frequencies for B and D
M1dep
12
A1
Alternative method
Page 7
The Oakwood Academy
Subtracts any pair of relative frequencies
M1
0.04 − 0.016 (× 500)
or 0.024
M1dep
12
A1
[3]
M3.
(a)
Q = Qualifies
D N Q = Does not qualify
B1 0.2 on DNQ branch
or
All branches included labelled correctly with Q and DNQ but
probabilities not all correct
B2
(b)
Alternative method 1
their 0.2 × their 0.8 or 0.16
Look on tree diagram for working
M1
0.96
Page 8
The Oakwood Academy
A1
Alternative method 2
(their 0.2)² or 0.04
Look on tree diagram for working
M1
0.96
A1
[4]
M4.
Mark the diagram first and only look in working space if
blanks in diagram.
P(B) = 0.4
B1
P(Not A) = 0.7 and 1 − their 0.4, and same probabilities on both second branches
B1ft
Any 1st event and 2nd event probability multiplied together
Follow through their values even if 0.7
wrong, but probabilities must be 0 p
M1
Page 9
The Oakwood Academy
Full correct final probabilities
ft their probabilities
A1ft
[4]
M5.
(a)
Shades the area outside the circles
B1
(b)
Shades all of A except the intersection with B
B1
[2]
Page 10