2. Probability Normal Distribution Sampling and Sample size
Benjamin Kamala

3. Probability
Proportional of times the event occurs in a long series of random numbers

4. E.g. tossing a coin once P(H) = ½, P(T) = 1/2
Tossing a dice (1,2,3,4,5,6)
P(1)=1/6, p(2)=1/6, p(3)=1/6……
Even numbers, E: 2,4,6
Prime number, O: 2,3,5
P(E)=3/6=1/2
P(O) = 1/2

5. Note Take values from 0 to 1
P= 0=event never occur, P=1=event certainly occurs
The sum of all probabilities = 1

6. Calculation
Additional rule:(A or B)=P(A)+P(B)-P(A and B)

7. Independent events
Occurrence of one event does not affect in anyway the occurrence of the other
When a coin and Dice are tossed together the occurrence of any number on the dice does not affect the occurrence of H/T
Rule: P(A and B) = P(A)*P(B)

8. If the coin and dice are tossed together:
Find the probability of getting a H and even number (E)
P(H)=1/2
P(E)=3/6=1/2
P(H and E) = ½*1/2=1/4

9. A pack of 52 playing cards: 13 spades, 13 hearths, 13 flowers, 13 Diamonds
If a two cards are picked (one at a time) in random manner what is the probability that both are Diamonds?
If a two cards are picked (one at a time) in random manner what is the probability that one is a Diamonds and another is a Spade?

10. Example
If Joshua and Hassan attend Biostatistics lectures only once in a month and there is one Biostatistics lecture per week; what is the probability of finding both of them in a given lecture
What is the probability of finding either of them in a given lecture

11. Mutually exclusive events: two events never occur together
P(A and B) = 0
E.g. when the coin is tossed once P(HnT) = 0

12. Two coins are tossed; find the probability that two heads are obtained.
Question 3: Which of these numbers cannot be a probability? 


a) 

b) 0.5 

c) 

d) 0 

e) 1
20%
Two dice are rolled, find the probability that the sum is
a) equal to 1
b) equal to 4 


c) less than 13

13. Examples
A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the coin shows a head.
A card is drawn at random from a deck of cards. Find the probability of getting the 3 of diamond
A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is white

14. Question 1: A die is rolled, find the probability that an even number is obtained
Question 2: Two coins are tossed, find the probability that two heads are obtained.
Question 4: Two dice are rolled, find the probability that the sum is  a) equal to 1  b) equal to 4  c) less than 13
Question 5: A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the coin shows a head
Question 6: A card is drawn at random from a deck of cards. Find the probability of getting the 3 of diamond.
Question 7: A card is drawn at random from a deck of cards. Find the probability of getting a queen.

15. Question 8: A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is white?

16. Question 9: The blood groups of 200 people is distributed as follows: 50 have type Ablood, 65 have B blood type, 70 have O blood type and 15 have type AB blood. If a person from this group is selected at random, what is the probability that this person has O blood type?

17. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

18. A bag contains 2 red, 3 green and 2 blue balls
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

19. What is the probability of getting a sum 9 from two throws of a dice?
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
What is the probability of getting a sum 9 from two throws of a dice?
Three unbiased coins are tossed. What is the probability of getting at most two heads?
A number X is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3. What is the probability that |X|<2
Two brother X and Y appeared for an exam. Let A be the event that X is selected and B is the event that Y is selected.
The probability of A is 17 and that of B is 29. Find the probability that both of them are selected.

20. Home Work
A card is drawn at random from a deck of cards. Find the probability of getting the King of heart. 
A bag contains 21 toys numbered 1 to 21. A toy is drawn and then another toy is drawn without replacement. Find the probability that both toys will show even numbers.
A speaks truth in 75% of cases and B in 80% of cases. In what percent of cases are they likely to contradict each other in narrating the same event?
What is the probability that a number selected from numbers 1,2,3,...,30, is prime number, when each of the given numbers is equally likely to be selected?