Question 183099This question is from textbook Study Guide: Review
: 13. The 10-number math team randomly selects 4 representatives to send to a meet. What is the probability that the 4 members chosen are the 4 with the lowest math grades?
14. A 5-digit code is given to all cashiers at a store to let them log onto the cash register. What is the probability that an employee receives a code with all 5 numbers the same?
Explain why the events are independent and find the probability.
25. rolling "doubles" 3 times in a row when rolling 2 number cubes
26. selecting a red pen and then a blue pen, when selecting 2 pens from a bag of 10 red and 15 blue pens with replacement
Could you explain how to solve it?
Thank you for your help.
This question is from textbook Study Guide: Review
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 13. The 10-number math team randomly selects 4 representatives to send to a meet. What is the probability that the 4 members chosen are the 4 with the lowest math grades?
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There are 10C4 = 210 sets of 4
There is only one set that has the 4 lowest math grades
P(4 lowest) = 1/210
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14. A 5-digit code is given to all cashiers at a store to let them log onto the cash register. What is the probability that an employee receives a code with all 5 numbers the same?
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Since repetition is allowed in the code there are 5^10 different codes.
There are 10 codes that have all digits the same: 00000,11111,...,99999
P(all digits are the same = 10/10^5 = 1/10^4 = 1/10,000
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Explain why the events are independent and find the probability
The events are independent because once you have selected a digit,
that digit is replaced for the next selection. No selection depends
on the previous selection.
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25. rolling "doubles" 3 times in a row when rolling 2 number cubes
P(doubles on one pair of dice) = 6/36 = 1/6
P(doubles on three separage rolls) = (1/6)^3 = 1/216
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26. selecting a red pen and then a blue pen, when selecting 2 pens from a bag of 10 red and 15 blue pens with replacement
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Number of red/blue pairs = 10*15 = 150
Number of unrestricted pairs: 25C2 = 300
P(red/blue pair) = 150/300 = 1/2
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Cheers,
Stan H.
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