Respuesta :
Answer:
(a) The probability that the student is a woman is 0.6591.
(b) The probability that the student received an A is 0.2045.
(c) The probability that a student selected is a woman or received an A is 0.75.
(d) The probability that a student did not receive an A is 0.7955.
Step-by-step explanation:
The total number of students in the class is, N = 44.
The number of men, n (M) = 15.
The number of women, n (W) = 29.
The number of men who receive an A is, n (M ∩ A) = 4.
The number of women who receive an A is, n (W ∩ A) = 5.
The number of students who received an A, n (A) = 9.
(a)
The probability that a randomly selected students is a woman is:
[tex]P(W)=\frac{n(W)}{N} =\frac{29}{44} =0.6591[/tex]
Thus, the probability that the student is a woman is 0.6591.
(b)
The probability that a randomly selected student received an A is:
[tex]P(A)=\frac{n(A)}{N} =\frac{9}{44}= 0.2045[/tex]
Thus, the probability that the student received an A is 0.2045.
(c)
The probability that a student selected is a woman or received an A is:
[tex]P(W\cup A)=P(W)+P(A)-P(W\cap A)\\=\frac{n(W)}{N}+\frac{n(A)}{N}-\frac{n(W\cap A)}{N} \\=\frac{29}{44}+\frac{9}{44}-\frac{5}{44}\\ =\frac{33}{44} \\=0.75[/tex]
Thus, the probability that a student selected is a woman or received an A is 0.75.
(d)
The probability that a student did not receive an A is:
[tex]P(A^{c})=1-P(A)\\=1-0.2045\\=0.7955[/tex]
Thus, the probability that a student did not receive an A is 0.7955.
