Question

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

Answer 1

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

`P=(3)/(4+5+3)=(3)/(12)`

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

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

Therefore the correct option is D.