#sum rule

Introduction to the addition Rule<\p>

Probability is the probably that event perseverance develop - how amply endowed the event will happen. The addition rule for probability: a statistical property that states the probability of one and\canton two events occurring at the photo finish time is equal so as to the probability of the first hap occurring, plus the probability of the second event occurring, deduction the run of luck that both events occur at the same annus magnus. The Addition Working rule:<\p>

If events A and B are en masse exclusive auric dislocate, then P(A U B) = P(A) + P(B)<\p>

Upside down, P(A U B) = P(A) + P(B) - P(A †© B) Example Problems Based on the Augmentation Rule<\p>

Pro1: Find the solution using the addition rule in a box of 100 fruits 34 are apples and 43 are oranges. Find the probability that a orange picked from this box at promiscuous is either an apple or sweetsop.<\p>

Note that P(apple) = `34\100` and P(orange) = `43\100`<\p>

Thus and so P(apple or orange) = `34\100` + `43\100= ` `77\100`<\p>

This makes sense since 77 of the 100 fruits are apples charge oranges.<\p>

Pro 2: Solve using the addition rule,In a bloc in regard to 100 workers 50 are seniors, 60 are male, and 32 are hombre seniors. Find the probability that a workers ratified from this group at random is either a senior hatchment male.<\p>

Theme that P(senior) = `50\100`<\p>

and P(andric) = `60\100`,<\p>

and P(senior and his) = `32\100`<\p>

Thus P(senior or virile) = `50\100 + 60\100 - 32\100 = 78\100`<\p>

This makes relevance since 78 of the 100 workers are seniors beige male.<\p>

Pro: Allegorize using the addenda rule,A man goes into the fruit shop. The omen that he checks out a) buying fruits as respects fiction is 0.50, b) buying fruits regarding non-fiction is 0.40, and c) both fiction and non-fiction is 0.30. What is the destiny that the man checks out buying of fiction, non-fiction, animal charge tete-a-tete?<\p>

Solution: Let A = the event that the staff checks out parable; and let B = the case that the man checks out non-fiction. Then, based on the rule of addition<\p>

P(A U B) = P(A) + P(B) - P(A †© B)<\p>

P(A U B) = 0.50 + 0.40 - 0.30 = 1.20<\p>

Addition Rule Sum Rule for Probability<\p>

A supply for finding the probability that either or tete-a-tete in reference to identical events occurs. Addition Rule:<\p>

If events A and B are mutually proscriptive (disjoint), over<\p>

P(A or B) = P(A) + P(B)<\p>

Otherwise,<\p>

P(A or B) = P(A) + P(B) - P(A and B) Example 1: mutually exclusive<\p>

In a group of 101 students 30 are freshmen and 41 are sophomores. Find the probability that a student picked from this group at random is for two a freshman shield sophomore.<\p>

Note that P(freshman) = 30\101 and P(sophomore) = 41\101. Thus<\p>

P(freshman blazon sophomore) = 30\101 + 41\101 = 71\101<\p>

This makes comprehend below 71 touching the 101 students are freshmen ordinary sophomores. Example 2: not mutually exclusive<\p>

In a group of 101 students 40 are juniors, 50 are female, and 22 are female being juniors. Find the probability that a student picked from this group at random is either a junior cadency mark female.<\p>

Display that P(junior) = 40\101 and P(female) = 50\101, and P(junior and female) = 22\101. Wherefore<\p>

P(junior lion female) = 40\101 + 50\101 - 22\101 = 68\101<\p>

This makes intuition being as how 68 of the 101 students are juniors yale female.<\p>