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 ​$533 check and three envelopes contain a ​$1039 check.

Answer 1

check 533×3= $1599.
envelopes- $1039 × 3 = $3117
so you add $1599 + $3117= $4716.00

Answer 2

Answer with explanation:

Number of Envelopes possessed by the person = 6

Probability of selecting an Envelope is equal to $/frac{1}{6}$.

It is given that,three envelopes contains $ 533 check and another 3 Envelope contain $ 1039 check.We can consider that any of three checks contain $ 533 and another three $ 1089.

Expectation

[tex]E(x)=x_{1}p_{1}+x_{2}p_{2}+x_{3}p_{3}+x_{4}p_{4}+x_{5}p_{5}+x_{6}p_{6}\\\\\frac{1}{6} \times [533+533+533+1039+1039+1039]\\\\=\frac{1}{6} \times [4716]\\\\=786[\tex]

E(x)=786