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Jillian surveyed students at her school and found out the following probabilities: P ( freshman ) = 0.30 P ( plays instrument ) = 0.20 P ( freshman and instrument ) = 0.10 ​ P(freshman)=0.30 P(plays instrument)=0.20 P(freshman and instrument)=0.10 ​ Find the probability that a student plays an instrument given they are a freshman. P ( plays instrument ∣ freshman ) =

Respuesta :

Answer: 1/3

Step-by-step explanation:

Cricetus

The probability that a student plays an instrument will be "0.33".

Given:

  • [tex]P(freshman) = 0.30[/tex]
  • [tex]P(Plays \ instrument) = 0.20[/tex]
  • [tex]P(Freshman \ \cap \ Instrument) = 0.10[/tex]

Now,

The probability that students plays instrument:

→ [tex]P(Plays \ instrument|Freshman) = \frac{P(Instrument \ \cap \ Freshman)}{P(Freshman)}[/tex]

By substituting the values, we get

                                                        [tex]= \frac{0.10}{0.30}[/tex]

                                                        [tex]= \frac{1}{3}[/tex]

                                                        [tex]= 0.33[/tex]

Thus the response above is right.      

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