Addition Rule for Non-Mutually Exclusive Events
When do we use the addition rule?
If we want to calculate the probability of event A occurring or event B occurring, taking into account that they are mutually exclusive, we use the addition rule.
Formula:
P(A or B) = P(A) + P(B) - P(A and B)
, where
P(A or B)
- the probability of event A occurring or event B occurring,P(A)
- the probability of event A occurringP(B)
- the probability of event B occurringP(A and B)
- the probability of events A and B occurring simultaneously
Task example:
In the class, there are 18 boys and 12 girls; 15 people have dark hair (3 girls and 12 boys). What is the probability of randomly choosing a girl or a dark-haired student?
P(girl)
= 12/30 = 0.4 = 40%P(dark-haired student)
= 15/30 = 0.5 = 50%P(girl and dark-haired student)
= 3/15 = 20%P(girl or dark-haired student)
=P(girl) + P(dark-haired student) - P(girl and dark-haired student) = 40% + 50% - 20%= 70%.
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Addition Rule for Non-Mutually Exclusive Events
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When do we use the addition rule?
If we want to calculate the probability of event A occurring or event B occurring, taking into account that they are mutually exclusive, we use the addition rule.
Formula:
P(A or B) = P(A) + P(B) - P(A and B)
, where
P(A or B)
- the probability of event A occurring or event B occurring,P(A)
- the probability of event A occurringP(B)
- the probability of event B occurringP(A and B)
- the probability of events A and B occurring simultaneously
Task example:
In the class, there are 18 boys and 12 girls; 15 people have dark hair (3 girls and 12 boys). What is the probability of randomly choosing a girl or a dark-haired student?
P(girl)
= 12/30 = 0.4 = 40%P(dark-haired student)
= 15/30 = 0.5 = 50%P(girl and dark-haired student)
= 3/15 = 20%P(girl or dark-haired student)
=P(girl) + P(dark-haired student) - P(girl and dark-haired student) = 40% + 50% - 20%= 70%.
Дякуємо за ваш відгук!