Question 73096: Please show me specific detailed answers to these question i got wrong on my test. Thankyou.
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.
B. What is the probability of getting strictly less than 3 questions wrong?
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).
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)
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)?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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)
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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
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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
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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
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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
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Cheers,
Stan H.
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