Two cards are drawn without replacement from an ordinary deck of 52 cards. What
ID: 3237266 • Letter: T
Question
Two cards are drawn without replacement from an ordinary deck of 52 cards. What is the probability that the cards are a diamond and a spade? You are building 16 digit passwords (numbers only). What is the probability that you create a password that has no repeated digits. A plant manufactures microchips, 5% of which are defective. The plant makes $18 on each good microchip and loses $23 on each defective one. What is the expected profit on a microchip? You play a game where you roll two six-sided dice and sum the pips showing. It costs you $2 to play the game. If your dice sum to 7 or 11, you win $20. If your dice sum to 2 or 12, you win $2. If your dice sum to any other number, you lose. a) What is your expected winnings for this game? b) Is the game fair? Why or why not? Consider the list: 21, 13, 2, 19, 23, 18, 5, 24, 21, 19, 4, 16, 20 Find the following. Give answers to 4 decimal places if rounding. a) Mean b) Median c) Mode d) Range e) Standard deviation f) VarianceExplanation / Answer
6. Probability of diamond or spade on 1st draw = 26/52 = 1/2
If the 1st draw is diamond, then probability of spade in 2nd draw = 13/51
If the 1st draw is spade, then probability of diamond in 2nd draw = 13/51
Total probability = (1/2)*(13/51) + (1/2)*(13/51) = 0.255
7. Total number of passwords = 10^16
Total number of Passwords of 16 digit length with no repeated digits = 0
Probability of Passwords of 16 digit length with no repeated digits = 0
8. Expected profit = 0.95 * $18 - 0.05 * $23 = $15.95
9. Probability of 7 or 11 = 8/36 = 2/9
Probability of 2 or 12 = 2/36 = 1/18
Probability of losing = 1 - (2/9+1/18) = 13/18
Expected winnings = $20 * 2/9 + $2 * 1/18 - $2 * 13/18 = $3.11
b) As the expected winnings is not 0, the game is not fair.
10. a) Mean = 15.77
b) Median = 19
c) Mode = 19 and 21
d) Range = 22
e) Standard deviation = 7.47
f) Variance = 55.85
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.