Question 73096
1. a. On a multiple choice test there are 6 questions and each question has 5 possible choices. If someone randomly guesses the answer for each question, what is the probability of getting exactly 5 questions wrong? Assume the answer has exactly 1 correct answer, and that the answer to any question is independent of the answer to any other question. Express your final answer as a decimal number rounded to 5 decimal places.
Binomial Problem
p=1/5; q=4/5 ;n=6
P(one answer correct) = 6C1(1/5)^1(4/5)^5 = 0.39
If you have a TI-83 it is binompdf(6,1/5,1)
---------------
B. What is the probability of getting strictly less than 3 questions wrong?
P(0<=X<=2) = binomcdf(6,1/5,2)=0.90 
=6C0(1/5)^0(4/5)^6 +6C1(1/5)^1(4/5)5+6C2(1/5)^2(4/5)^4
----------------

2. The suits in a deck of cards are: Clubs, Diamonds, Hearts and Spades.
   The 13 ranks are (lowest to highest): 2 3 4 5 6 7 8 9 10 (J)ack, (Q)ueen, (K)ing, (A)ce. There are 4 suits and 13 ranks thus there are 4x13=52 possible combinations. 
Ace-clubs, 6-spades, J-hearts, king-hearts, 10-diamonds, 8-spades, Ace-spades, Queen-hearts, Ace-heearts, 7-spades, King-clubs, 3-Diamonds, 4-diamonds, 5-spades.
 If you selected 1 card at random from the above 14 cards calculate the probability of...

a. Getting a heart or a card with a rank of K or higher? (Round final answer 3 decimal places).
P(heart or K or Ace) = (4+2+3-2)/14 = 1/2
There are 4 hearts; 2 kings; 3 Aces ; but 2 card that are both K/A and heart
----------------

b. Getting a card which is not a spade or a card with a rank of A or higher?
(Round final answer to 3 decimal places)
 = 1-P(spade or Ace)
 = 1-(5+3-1)/14 = 1 - 1/2 = 1/2
----------------
3. A charitable organization is selling raffle tickets for 5$. The first prize is a stereo system valued at $2,710. Second prize is an electric scooter valued at $970.00. The remaining prizes are 35 third prize gift certificates each valued at $40. Suppose 3500 tickets were sold, and you bought 1 ticket, what is the expected value of your net gain (or loss)? 
E(gain) = (1/3500)(2710+970+35*40)-(3463/3500)(5)=1.45-4.95=-$3.50
You can expect to lose $3.50
-------------------------
Cheers,
Stan H.