Presentation of probability, addition rule presentation, multiplication rule presentation, conditional rule presentation

2. Please wait
LOADING

3. Presentation Title
Your company information
PROBABLITIY
PRESENTATION
PRESENTED TO:
SIR UMER SAEED

4. GROUP MEMBERS
 KAYNAT AKMAL
 M. OSAMA SAEED KHAN
 TAIMOOR EJAZ
 MUHAMMAD AAMIR MANZOOR

5. CONTENTS
 CONDITIONAL PROBABILITY
 JOINT PROBABLITY
 ADDITION RULE
GO TO
CONDITIONAL
JOINT
ADDITION

6. CONDITIONAL
PROBABILITY

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

8. SOLUTION
Suppose Event A is matric pass male
Event B is total male
We have to find
P(A |B)

9. SOLUTION
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

12. i. P(M│R) = ?
ii. P (F│L) = ?
SOLUTION

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?

16. TREE DIAGRAM

17. SOLUTION

18. SOLUTION

19. JOINT
PROBABILITY

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

21. SOLUTION
i. Win both
1
1245
×
1
324
=
1
403380
ii. Wins one but not both
1
1245
×
323
324
+
1244
1245
×
1
324
= 0.0320

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

27. ADDITION
RULE

28. EXAMPLE 1
A single card is chosen at random from a standard deck of 52
playing cards. What is the probability of choosing a king or a
club?

29. Suppose Event A is choosing card is KING
Event A is choosing card is CLUB
We have to find P(A∪B)
SOLUTION

30. DISTRIBUTION OF PLAYING CARDS
SPADES=13
HEARTS=13
DIAMONDS=13
CLUBS=13
52
ACE 2 3 4 5 6 7 8 9 10 JACK QUEEN KING
Red=26

31. As these two events are non-mutually exclusive so
𝑃 𝐴 ∪ 𝐵 = 𝑃 𝐴 + 𝑃 𝐵 − 𝑃(𝐴 ∩ 𝐵)
Also
𝑃 𝐴 ∪ 𝐵 = 𝑃 𝐴 + 𝑃 𝐵 − [𝑃(𝐴) × 𝑃(𝐵│A)]
SOLUTION

32. 𝑃 𝐴 ∪ 𝐵 =
4
52
+
13
52
−
1
52
𝑃 𝐴 ∪ 𝐵 =
16
52
=
4
13
SOLUTION

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

34. 𝑃 𝑖𝑛𝑡𝑜𝑥𝑖𝑐𝑎𝑡𝑒𝑑 = 0.32
𝑃 𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡 = 0.09
𝑃 𝑖𝑛𝑡𝑜𝑥𝑖𝑐𝑎𝑡𝑒𝑑 𝑎𝑛𝑑 𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡 = 0.15
𝑃 𝑖𝑛𝑡𝑜𝑥𝑖𝑐𝑎𝑡𝑒𝑑 𝑜𝑟 𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡 =?
SOLUTION

35. 𝑃 𝑖𝑛𝑡𝑜𝑥𝑖𝑐𝑎𝑡𝑒𝑑 𝑜𝑟 𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡 = 𝑃 𝑖𝑛𝑡𝑜𝑥𝑖𝑐𝑎𝑡𝑒𝑑 +
𝑃 𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡 − 𝑃 𝑖𝑛𝑡𝑜𝑥𝑖𝑐𝑎𝑡𝑒𝑑 𝑎𝑛𝑑 𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡
𝑃 𝑖𝑛𝑡𝑜𝑥𝑖𝑐𝑎𝑡𝑒𝑑 𝑜𝑟 𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡 = 0.32 + 0.09 − 0.15
𝑃 𝑖𝑛𝑡𝑜𝑥𝑖𝑐𝑎𝑡𝑒𝑑 𝑜𝑟 𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡 = 0.26
SOLUTION

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

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

42. Thank You