Statistics grades: In a statistics class ofstudents, there weremen andwomen. Four of the men and five of the women received an A in the course. A student is chosen at random from the class.(a) Find the probability that the student is a woman.(b) Find the probability that the student received an A.(c) Find the probability that the student is a woman or received an A.(d) Find the probability that the student did not receive an A.

(a) The probability that the student is a woman is .

(b) The probability that a randomly selected student received an A is .

(c) The probability that a student selected is a woman or received an A is .

(d) The probability that a students selected did not receive an A is .

Step-by-step explanation:

Let's assume that there were N students in a class.

Also assume that there are n₁ men and n₂ women in the class.

Let's denote M = a student is a man, W = a student is a woman and A = a student received an A in the course.

It is provided that 4 men and 5 women received an A in the course.

The probability that a student is a man and he received an A is,

The probability that a student is a woman and she received an A is,

(a)

There are n₂ students in the class who are female.

The probability that the student is a woman is,

(b)

The total number of students who received an A is, 9.

The probability that a randomly selected student received an A is:

(c)

The probability that a student selected is a woman or received an A is:

P (W ∪ A) = P (W) + P(A) - P(W ∩ A)

(d)

The probability that a students selected did not receive an A is:

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363

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