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Lottery profits, Probability Distribution, Mary's grades this semester

Please provide step by step solution.

Instructions: Solve the following problems keep the guidelines below in check.

If you are calculating something using a table, the number of decimal places from the table is expected. like z=1.00, table value is .8413 (2 decimal places for z, 4 for the probability)
REGARDING NUMBER OF DECIMAL PLACES:
IF AN ANSWER CALLS FOR 4 DECIMAL PLACES (FOR EXAMPLE), CALCULATE TO 5 DECIMAL PLACES AND ROUND TO 4.

1) The local lottery sets up a game wherein a player has a chance of collecting $800.
The player must choose a 3-digit number and if it matches the lottery number, the player receives $800
000 is a 3-digit number for lottery draws. (as are 001, 023, etc.)
It costs $2 to play the game.
What is each player's expected profit (or loss).
The AVERAGE!
No words, if it's a loss of $0.02, write it as -$0.02
NOT loss of 2 cents.
The FORMAT that is expected :
$4.00, -$4.00 etc. (Neither of which is the correct answer!)
NO, $-4.00 would NOT be correct...even if -$4 were the correct answer)
2 decimal places required. It's money!

2) Complete the following Probability Distribution. Then calculate the mean (2 decimal places). If impossible to calculate, write in 0 (zero) for the mean. Your answer should be the mean (not the value you used to complete the distribution)
x | P(x)
0 | .40
1 | .20
2 | 0.13
3 | ?

3) The probability Mary will receive an A in a class is 0.42.
Assuming independence, if she is taking 5 classes this semester, calculate the probability she will receive exactly 3 A's.
(4 decimal places) YES, you need, therefore, to look at the 5th decimal place.

Solution Summary

The expert examines the probability distribution for the lottery profits and Mary's grades this semester.

$2.19