Question

A person randomly selects one of six envelopes Each envelope contains a check that the person gets to keep. Determine the person's expectation if three envelopes contain a 491 check and three envelopes contain a 51003 checkThe expected value is $(Simplify your anwwer Type an integer or a decimal)

Answer 1

The probability formula is given by:

$\text{ P(E) =}\frac{\text{ N(Required outcome)}}{\text{ N(Total outcome)}}$

The person selects one of six envelopes.

There is a probability that the person selects an envelope that contains a $491 of 3 envelopes OR an envelope that contains a $1003 check of 3 envelopes

$\begin{gathered} \text{ P(select one containing \ 491 check) =}\frac{3}{6}=\frac{1}{2} \\ \text{ P(select one containing \ 1003 check) =}\frac{3}{6}=\frac{1}{2} \end{gathered}$

Then, the expected value is given by

$\begin{gathered} \text{ P(Expected Value) =(}\frac{1}{2}\times491)\text{ +(}\frac{1}{2}\times1003) \\ =245.5+501.5 \\ =747.0 \end{gathered}$