Respuesta :
Answer:
The probability that a student is selected ta random is a man or received an A in the exam is 0.5714.
Step-by-step explanation:
In a class of 35 students there are 20 women and 15 men.
Compute the probability of selecting a men as follows:
[tex]P(M)=\frac{15}{35}[/tex]
Compute the probability of selecting a women as follows:
[tex]P(W)=\frac{20}{35}[/tex]
It is provided that 5 women and 4 men received A’s in the first exam.
Compute the probability of a a student getting an A and the student being a man as follows:
[tex]P(A\cap M)=\frac{4}{35}[/tex]
Compute the probability of a a student getting an A and the student being a woman as follows:
[tex]P(A\cap W)=\frac{5}{35}[/tex]
Compute the probability of a student receiving an A as follows:
[tex]P(A)=P(M\ca A)+P(W|cap A)=\frac{4}{35}+\frac{5}{35} =\frac{9}{35}[/tex]
Compute the probability that a student is selected ta random is a man or received an A in the exam as follows:
[tex]P(M\cap A) = P(M) + P(A) - P (M\cap A)\\=\frac{15}{35}+\frac{9}{35}-\frac{4}{35}\\ =\frac{15+9-4}{35}\\ =\frac{20}{35}\\=0.571429\\\approx0.5714[/tex]
Thus, the probability that a student is selected ta random is a man or received an A in the exam is 0.5714.
