KathrynG409428 KathrynG409428
  • 26-10-2022
  • Mathematics
contestada

Suppose that E and F are two events and that P(E) = 0.3 and P(F/E) = 0.9What is P(E and F)?

Suppose that E and F are two events and that PE 03 and PFE 09What is PE and F class=

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DaisyH184295 DaisyH184295
  • 26-10-2022
Probability

We want to find P (E ∩ F)

We know that

[tex]P(F|E)=\frac{P(F\cap E)}{P(E)}[/tex]

Multiplying P ( E ) both sides, we find the P (E ∩ F) equation:

[tex]P(E)P(F|E)=P(F\cap E)[/tex]

Replacing P( E ) = 0.3 and P( F | E ) = 0.9, we find that

[tex]\begin{gathered} P(F\cap E)=P(E)P(F|E) \\ P(F\cap E)=0.3\cdot0.9 \\ P(F\cap E)=0.27 \end{gathered}[/tex]

Answer: D. 0.27

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