Question

A PAPPER BAG CONTAINS THREE $1.00 BILLS, TWO FIVE DOLLAR BILLS, SIX TEN DOLLAR BILLS AND ONE TWENTY DOLLAR BILL. MARK MAY SELECT AND KEEP ONE BILL FROM THE BAG. FIND MARKS EXPECTED GAIN?

Answer 1

Given

number of $1.00 bills = 3

number of $5.00 bills = 2

number of $10.00 bills = 6

number of $20.00 bills = 1

Find

expected gain

Step-by-step explanation

Total number of bills = 3 + 2 + 6 + 1 = 12

P(X = 1) = 3/12 = 0.25

P(X = 5) = 2/12 = 0.1667

P(X = 10) = 6/12 = 0.5

P(X = 20) = 1/12 = 0.0833

so , the expected gain =

`\sum_^xP(x)`

therefore ,

E(X) =

`\begin{gathered} 1*0.25+5*0.1667+10*0.5+20*0.0833 \\ 0.25+0.8335+5+1.666 \\ 7.75 \end{gathered}`

Final Answer

Hence , the expected gain of Mark is 7.75