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17 October, 19:44

In a large school, it was found that 71% of students are taking a math class, 77% of student are taking an English class, and 58% of students are taking both. Find the probability that a randomly selected student is taking a math class or an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.

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  1. 17 October, 19:57
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    P (Math or English) = 0.90

    Step-by-step explanation:

    * Lets study the meaning of or, and on probability

    - The use of the word or means that you are calculating the probability

    that either event A or event B happened

    - Both events do not have to happen

    - The use of the word and, means that both event A and B have to

    happened

    * The addition rules are:

    # P (A or B) = P (A) + P (B) ⇒ mutually exclusive (events cannot happen

    at the same time)

    # P (A or B) = P (A) + P (B) - P (A and B) ⇒ non-mutually exclusive (if they

    have at least one outcome in common)

    - The union is written as A ∪ B or "A or B".

    - The Both is written as A ∩ B or "A and B"

    * Lets solve the question

    - The probability of taking Math class 71%

    - The probability of taking English class 77%

    - The probability of taking both classes is 58%

    ∵ P (Math) = 71% = 0.71

    ∵ P (English) = 77% = 0.77

    ∵ P (Math and English) = 58% = 0.58

    - To find P (Math or English) use the rule of non-mutually exclusive

    ∵ P (A or B) = P (A) + P (B) - P (A and B)

    ∴ P (Math or English) = P (Math) + P (English) - P (Math and English)

    - Lets substitute the values of P (Math), P (English), P (Math and English)

    in the rule

    ∵ P (Math or English) = 0.71 + 0.77 - 0.58 ⇒ simplify

    ∴ P (Math or English) = 0.90

    * P (Math or English) = 0.90
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