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Rule of Complements When randomly selecting an adult, let B represent the event of randomly selecting someone with type B blood. Write a sentence describing what the rule of complements is telling us:PBorB=1

Short Answer

Expert verified

PBorB=1tells that either a randomly selected person will have blood type B or they will not have blood type B.

In other words, one of the two events B andB will surely occur.

Step by step solution

01

Given information

Let B be the event of selecting a person with type B blood.

02

Rule of probability for complementary events

If A represents the occurrence of an event and Arepresents the occurrence of 鈥渘ot A,鈥 then A andA arecomplementary events.

The outcomes that do not belong to event A belong to the complementary set and vice-versa. Consequently, only one of the two events can occur at one point in time.

Moreover, one of the two events is sure to occur.

Mathematically,

PAorA=PA+PA=1

03

In terms of given event B

Here, B is the event of selecting a person with type B blood. Then, is the event of selecting a person whose blood type is not B.

Thus, the probability that either of the two events will occur is given as:

PBorB=PB+PB-PBandB...Additionrule=PB+PB-0=PB+PB=1

This implies that events B andB cannot occur together, and either of the two events will certainly occur.

Specifically, the probability that a person either has blood type B or does not have blood type B is sure to occur for any randomly selected adult.

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