Respuesta :
Answer:
The exact probability that the student selected is a junior whose favorite subject is Math is [tex]\frac{124}{459}[/tex].
Step-by-step explanation:
Let the following events represents by the alphabets A and B.
A: Student selects Math as the favorite subject
B: Student chosen is a junior
The probability that the student selects Math as the favorite subject is 1/4.
[tex]P(A)=\frac{1}{4}[/tex]
The probability that the student chosen is a junior is
[tex]P(B)=\frac{116}{459}[/tex]
The probability that the student selected is a junior or that the student chooses Math as the favorite subject is 47/108.
[tex]P(A\cup B)=\frac{47}{108}[/tex]
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
[tex]\frac{47}{108}=\frac{1}{4}+\frac{116}{459}-P(A\cap B)[/tex]
[tex]P(A\cap B)=\frac{1}{4}+\frac{116}{459}-\frac{47}{108}=\frac{31}{459}[/tex]
The exact probability that the student selected is a junior whose favorite subject is Math is
[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]P(\frac{B}{A})=\frac{\frac{31}{459}}{\frac{1}{4}}=\frac{124}{459}[/tex]
Therefore the exact probability that the student selected is a junior whose favorite subject is Math is [tex]\frac{124}{459}[/tex].
The exact probability that the student selected is a junior whose favourite subject is maths is 124/459
What is probability?
It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
The probability that the student selects Maths the favourite subject:
P(A) = 1/4
The probability that the student chosen is a junior:
P(B) = 116/459
The probability that the student selected is a junior or that the student chooses maths the favourite subject:
P(A∪B) = 47/108
We know:
P(A∩B) = P(A) + P(B) _P(A∪B)
P(A∩B) = 1/4 + 116/459 - 47/108
P(A∩B) = 31/459
The exact probability that the student selected is a junior whose favourite subject is maths:
P(B|A) = P(A∩B) /P(A)
= (31/459)/(1/4)
= 124/459
Thus, the exact probability that the student selected is a junior whose favourite subject is maths is 124/459
Learn more about the probability here:
brainly.com/question/11234923
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