The probability of any event is the sum of the probabilities of the outcomes making up the event.
Ex 4.10 Accidents on weekends
accidents on weekends – P(sat or sun) = P(sat) +P(sun) = 0.02+0.03 = 0.05
Ex 4.13 How to find Benford’s law?
A = 1 P(A) = P(1) = 0.301
B = 6 p(B) = p(6) + P (7) + P(8) + P(9) = 0.222
-P(6) is included when B is = 6. But when B > 6 then P(6) is not included in the sum.
When probabilities are not disjoint, the sum addition rule cannot be applied
P( C)= p(1) + p(3) +p(5)
P(B) = p(3) + p(4) + p(5)
P( B or C) = p(1) + p(3) + p(4) + p(5)
•Non disjoint probabilities are only added once
Assigning probabilities: equally likely outcomes
Equally likely outcomes
If a random phenomenon has k possible outcomes, all equally likely, then each individual
outcome has probability 1/k. The probability of any event A is
P(A) = count of outcomes in A = count of outcomes in A
count of outcomes in S k
Independence and the multiplication rule
The multiplication rule for independent events
The events A and B are not disjoint – meaning the have the same outcomes
Rule 5: Two events A and B are independent if knowing that one occurs does not change the
probability that the other occurs. IF A and B are independent, P(A and B) = P(A)P(B)
Ex 4.16 Probability model that is independent is coin tossing; first toss doesn’t affect the second
Ex 4.17 Probability model that is dependent is picking up a card with the same color either red or
black from the deck.
Picking up a red card is 26/52 = 0.50. Once the first red card is picked, only 25 reds remain
among the 51 cards. Probability that the second card is red is 25/51 = 0.49.
•Knowing the outcome of the first card deal changes the probabilities for the second.