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Sagot :
Given:
Teenagers who own a game console = 46%
Teenagers who own a personal computer = 35%
Teenagers who own both a game console and personal computer = 29%
Required- the conditional probability that a teenager randomly selected owns a game console, given that the teenager owns a personal computer.
Explanation:
Let A be the event that the teenager randomly selected owns a game console.
Let B be the event the teenager randomly selected owns a personal computer.
Now, we change the probability of each event in decimal as:
[tex]\begin{gathered} P(A)=46\% \\ \\ =\frac{46}{100} \\ \\ =0.46 \end{gathered}[/tex]Now, the probability of event B is:
[tex]\begin{gathered} P(B)=35\% \\ \\ =\frac{35}{100} \\ \\ =0.35 \end{gathered}[/tex]Now, the probability of events A and B is:
[tex]\begin{gathered} P(A\text{ and B})=29\% \\ \\ =\frac{29}{100} \\ \\ =0.29 \end{gathered}[/tex]We know that the formula to find the conditional probability of event A, given event B is:
[tex]P(A|B)=\frac{P(A\text{ and B})}{P(B)}[/tex]Now, we put the given values in the formula, we get:
[tex]\begin{gathered} P(A|B)=\frac{0.29}{0.35} \\ \\ =0.82857 \\ \\ \approx0.83 \end{gathered}[/tex]Final answer: The conditional probability that a teenager randomly selected owns a game console, given that the teenager owns a personal computer is approximately 0.83.
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