MATH SOLVE

4 months ago

Q:
# 4. A student is chosen at random from the student body at a given high school. The probability that thestudent selects Math as the favorite subject is 1/4. The probability that the student chosen is a junior is116/459. If the probability that the student selected is a junior or that the student chooses Math as thefavorite subject is 47/108, what is the exact probability that the student selected is a junior whosefavorite subject is Math?

Accepted Solution

A:

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 subjectB: Student chosen is a juniorThe 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].