Probability Md Kamrul Hasan Associate Professor Ag Ext

Probability Md Kamrul Hasan Associate Professor Ag. Ext. & Rural Dev. , PSTU

Probability • ~ is the likelihood or chance that an event occurs. • Number total event = N • Number particular event = n • Probability of that particular event = n/N • Ranges from 0 to 1 or 0% to 100% • 0 = impossibility, 1 = certainty • e. g. Probability of male is 0. 50 in Bangladesh. • e. g. Probability of landing

Table shows the number of children with obesity 1. What is the probability of selecting a boy? 2. What is the probability of selecting a 7 year old? 3. What is the probability of selecting a boy who is 10 years of age? 4. What is the probability of selecting a child (boy or girl) who is at least 8 years of age?

Rules of probability • Addition rule: • Probability of occurring either event is the sum of all probabilities. • P(A or B) = P(A) + P(B) • Subtraction rule: • Probability of not occurring either event is the sum of all probabilities minus probability of occurring. • P(Female) = P(Male or Female) - P(Male)

Problem • Example 1: • the probability that Bill will graduate from college is 0. 80. What is the probability that Bill will not graduate from college? Based on the rule of subtraction, the probability that Bill will not graduate is 1. 00 - 0. 80 or 0. 20. • Example 2: • Probability of red, P(R) =. 3, Probability of black, P(B) =. 2 • P(R or B) = ?

Multiplication rule • Conditional probability: P(A|B) = P of A given that B has occurred • Multiplication rule = Probability of occurring both events A and B • P(A and B) = P(A). P(B) • If event B is dependent on A: P(A and B) = P(A). P(B|A) • Note that, conditional probability, P(B|A) = P(A and B)/P(A)

Problems • Example 1 • An urn contains 6 red marbles and 4 black marbles. Two marbles are drawn without replacement from the urn. What is the probability that both of the marbles are black? • Example 2 • A card is drawn randomly from a deck of ordinary playing cards. You win $10 if the card is a spade or an ace. What is the probability that you will win the game?