7. EXAMPLE 1
A survey of a small village show the following observations
Find the probability of Matric Pass given that Male
Matric Pass Intermediate Pass total
Male 45 30 75
Female 35 15 50
80 45 125
10. EXAMPLE 2
Consider the following contingency table
Find the probability that a randomly selected is
Male given right handed
A female given left handed.
RIGHT HANDED LEFT HANDED
MALE 0.41 0.08 0.49
FEMALE 0.45 0.06 0.51
0.86 0.14 1
11. SOLUTION
• Suppose M event is total male
F event is total female
R event is right handed &
L event is left handed
13. SOLUTION
i. P(M│R) =
𝑟𝑖𝑔ℎ𝑡 ℎ𝑎𝑛𝑑𝑒𝑑 𝑚𝑎𝑙𝑒
𝑡𝑜𝑡𝑎𝑙 𝑟𝑖𝑔ℎ𝑡 ℎ𝑎𝑛𝑑𝑒𝑑
P(M│R) =
0.41
0.86
P(M│R) = 0.48
RIGHT HANDED LEFT HANDED
MALE 0.41 0.08 0.49
FEMALE 0.45 0.06 0.51
0.86 0.14 1
14. SOLUTION
i. P(F│L) =
𝐿𝑒𝑓𝑡 ℎ𝑎𝑛𝑑𝑒𝑑 𝑓𝑒𝑚𝑎𝑙𝑒
𝑡𝑜𝑡𝑎𝑙 𝑙𝑒𝑓𝑡 ℎ𝑎𝑛𝑑𝑒𝑑
P(F│L) =
0.06
0.14
P(F│L) = 0.43
RIGHT HANDED LEFT HANDED
MALE 0.41 0.08 0.49
FEMALE 0.45 0.06 0.51
0.86 0.14 1
15. EXAMPLE 3
Weather records indicate that the probability that a particular day is dry is 3/10.
Arid FC is a football team whose record of success is better on dry days than
on wet days. The probability that Arid will win on a dry day is 3/8, whereas the
probability that the win a wet day is 3/11. Arid are due to play their next match
on Saturday.
What is the probability that Arid will win?
Three Saturdays ago Arid won their match. What is the probability that it
was a dry day?
20. EXAMPLE 1
The probability that a person wins a daily draw is 1/1245 and the
probability that a person wins a weekly draw is 1/324. Taimoor
participates in both draws. Find the probability that Taimoor
i. Wins both
ii. Wins one but not both
22. EXAMPLE 2
Mr. Aamir figures that there is a 30 percent chance that his
company will set up a branch office in Phoenix. If it does, he is 60
percent confirm that he will be made manager at this new
operation, what
• What is the probability that Aamir will be a Phoenix branch
office manager?
23. SOLUTION
P (B&M) = P (B) × P (M/B)
P (B&M) = (0.3) × (0.6)
P (B&M) = 0.18
24. A survey shows the following observation
EXAMPLE 3
DOING A JOB JOBLESS
MALE 41 8 49
FEMALE 20 31 51
61 39 100
If a randomly person is selected than what will be the probability
that selected person is male and doing a job?
25. Suppose Event M is male
Event J is doing a job
We have to find P(M&J)
SOLUTION
26. P(M&J) = P(M) × P(J│M)
P(M&J) =
49
100
×
41
49
P(M&J) =
41
100
= 0.41
SOLUTION
DOING A JOB JOBLESS
MALE 41 8 49
FEMALE 20 31 51
61 39 100
PROBABILITY
OF MALE
33. On New Year's Eve, the probability of a person having a car
accident is 0.09. The probability of a person driving while
intoxicated is 0.32 and probability of a person having a car
accident while intoxicated is 0.15.
What is the probability of a person driving while intoxicated or
having a car accident?
EXAMPLE 2
36. A survey shows the following observation.
Event
Event C D Total
A 4 2 6
B 1 3 4
Total 5 5 10
Find P(A D)
EXAMPLE 3
37. 𝑃 𝐴 ∪ 𝐷 = 𝑃 𝐴 + 𝑃 𝐷 − 𝑃(𝐴 ∩ 𝐷)
𝑃 𝐴 ∪ 𝐷 =
6
10
+
5
10
−
2
10
𝑃 𝐴 ∪ 𝐷 =
9
10
SOLUTION
Event
Event C D Total
A 4 2 6
B 1 3 4
Total 5 5 10
38.
39. CONDITIONAL PROBABILITY
The probability that it is Friday and that a student is absent is
0.03. Since there are 5 school days in a week, the probability that
it is Friday is 0.2. What is the probability that a student is absent
given that today is Friday?
Solution:
40. JOINT PROBABILITY
A box contains 10 balls out of which 5 are Red, 3 are Blue and 2
are white.
What would be the probability of getting red and blue ball?
SOLUTION:
As these events are independent so
𝑃 𝑅𝑒𝑑&𝑏𝑙𝑢𝑒 = 𝑃 𝑅𝑒𝑑 × 𝑃 𝐵𝑙𝑢𝑒
𝑃 𝑅𝑒𝑑&𝑏𝑙𝑢𝑒 =
5
10
×
3
10
=
3
20
41. ADDITION RULE
A spinner has 4 equal sectors colored yellow, blue, green, and red.
What is the probability of landing on red or blue after spinning this
spinner?
SOLUTION:
𝑃 𝑅𝑒𝑑 =
1
4
𝑃 𝐵𝑙𝑢𝑒 =
1
4
𝑃 𝑅𝑒𝑑 𝑜𝑟 𝐵𝑙𝑢𝑒 = 𝑃 𝑅𝑒𝑑 + 𝑃 𝐵𝑙𝑢𝑒 − 𝑃 𝑅𝑒𝑑&𝐵𝑙𝑢𝑒
As both event are mutually exclusive so P(Red & Blue) = 0
𝑃 𝑅𝑒𝑑 𝑜𝑟 𝐵𝑙𝑢𝑒 =
1
4
+
1
4
=
1
2
