To play a particular gambling machine, you put in $1 for each game. The machine

Question

To play a particular gambling machine, you put in $1 for each game. The machine claims a 1 in 6 chance of paying out $4 in any game: otherwise there is zero payout. Thus there are 2 possibilities: win a game you gain a net $3 and if you lose a game you lose a net $1. What is your expected profit (negative if it is a loss) if you play 7 games? State your answer in dollars, to the nearest cent. Do not include the dollar sign in your answer. A full time 1st year student at university takes 4 units per semester. The probability distribution function for the number of units in which you will achieve a grade of distinction (D) is: What is the expected number (mean) of distinction grades for a full-time 1st year student? State your answer to two(2) decimal places only.

Explanation / Answer

P(x =3) = 1/6

P(X = -1) = 5/6

E(X) = 1/6*3-5/6= 3/6-5/6 =-2/6 =-1/3

in 7 games

E(7X) = 7 *(-1/3) = -7/3=-2.333

8) E(X) = 0*0.1 +1*0.46 + 2*0.24 + 3*0.15 +4*0.05

= 1.59

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