Question

Giving a test to a group of students, the grades and ages are summarized below A B CTotalUnder 25419204325 or over1116532Total 15 35 2575If one student is chosen at random,Find the probability that the student was under 25 OR got an "B".

Answer 1

Let the event that the students were under 25 be A and the event that the student got a "B" be B.

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

Using the tables, we can find that:

`\begin{gathered} P(A)=(43)/(75) \\ P(B)=(35)/(75) \\ P(A\cap B)=(19)/(75) \end{gathered}`

Therefore,

`P(A\cup B)=(43)/(75)+(35)/(75)-(19)/(75)=(43+35-19)/(75)`

Thus,

`P(A\cup B)=(59)/(75)`

Therefore, the probability that the student was under 25 OR got an "B" is 59/75.

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