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The door prizes at a dance are gift certificates from local merchants. There are four $10 certificates, five $20 certificates, and three $50 certificates. The prize envelopes are mixed together in a bag and are drawn at random. What is the expected number of $50 certificates among the first three prizes drawn? A: 1B: 1.75C: 3D: 0.75

Respuesta :

In order to calculate the expected value in the first three prizes, let's first calculate the probability of a $50 certificate being drawn:

[tex]P=\frac{3}{4+5+3}=\frac{3}{12}[/tex]

Now, to find the expected value, we multiply the probability by the number of times the event is occurring:

[tex]\begin{gathered} E(x)=P\cdot n \\ E(x)=\frac{3}{12}\cdot3=\frac{9}{12}=\text{0}.75 \end{gathered}[/tex]

Therefore the correct option is D.

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