Question

In: Statistics and Probability

4.6/16. Many newspapers carry a certain puzzle in which the reader must unscramble letters to form...

4.6/16. Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words. How many ways can the letters of COUYPC be​ arranged? Identify the correct​ unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.

How many ways can the letters of COUYPC be​ arranged?

What is the correct unscrambling or COUYPC?

What is the probability of coming up with the correct unscrambling throughrandom letter selection?

19. Winning the jackpot in a particular lottery requires that you select the correct two numbers between 1 and 30 ​and, in a separate​ drawing, you must also select the correct single number between 1 and 34. Find the probability of winning the jackpot.

The probability of winning the jackpot is____

​(Type an integer or simplified​ fraction.)

20. Winning the jackpot in a particular lottery requires that you select the correct three numbers between 1 and 63 ​and, in a separate​ drawing, you must also select the correct single number between 1 and 52. Find the probability of winning the jackpot.

The probability of winning the jackpot is____

​(Type an integer or simplified​ fraction.)

Solutions

Expert Solution

4.6/16. This is a permutation with indistinguishable events - repeated items. The number of different permutations of objects, where there are indistinguishable objects of style 1, indistinguishable objects of style 2, ..., and indistinguishable objects of style k,

In this case, C O U Y P C , there are 2 Cs, 1 O, 1 U, 1 Y and 1 P.

So, and

Therefore, the number of ways in which letters of C O U Y P C can be arranged is ways

The correct unscrambling of C O U Y P C is

the probability of getting that result by randomly selecting one arrangement of the given letters is since there is only 1 correct unscrambling

19. Let us assume that the correct two numbers between 1 and 30 to win the jackpot are '16' and '28'. The correct single number between 1 and 34 to win the jackpot is '32'.

No. of ways in which any 2 random numbers can be chosen from 1 to 30 is ways

No. of ways in which any 1 random number can be chosen from 1 to 34 is ways

No. of possible outcomes = ways

Now, there is only one way in which '16' and '28' are chosen from 1 to 30 and '32' is chosen between 1 to 34.

Therefore, the probability of winning the jackpot is

20. Let us assume that the correct three numbers between 1 and 63 to win the jackpot are '21' , '45' and '58'. The correct single number between 1 and 52 to win the jackpot is '32'.

No. of ways in which any 3 random numbers can be chosen from 1 to 63 is ways

No. of ways in which any 1 random number can be chosen from 1 to 34 is ways

No. of possible outcomes = ways

Now, there is only one way in which '21' , '45' and '58' are chosen from 1 to 63 and '32' is chosen between 1 to 52.

Therefore, the probability of winning the jackpot is


Related Solutions

*PERMUTATIONS* How many tablets of 3 letters and 3 numbers can we form with the letters...
*PERMUTATIONS* How many tablets of 3 letters and 3 numbers can we form with the letters {A, B, C, D, E} and the 10 digits if the tablet should have: ◦ Letters and numbers should be kept together without repetition? ◦ Letters and numbers should be kept together with repetition? ◦ Letters and numbers do not have to be kept together without repetition? ◦ Letters and numbers do not have to be kept together with repetition?
How many distinct arrangements of the letters in MANANGATANG are there in which the first two...
How many distinct arrangements of the letters in MANANGATANG are there in which the first two letters include an M or a T (or both)? Note: - MANANGATANG has 11 letters (one M, one T, two Gs, three Ns and four As). - These are all the possible positionings of T and M in the first two positions: M M T T M T T M PLEASE SHOW FULL LEGIBLE WORKING.
Many insurance companies carry a deductible provision that states how much of a claim you must...
Many insurance companies carry a deductible provision that states how much of a claim you must pay out of pocket before the insurance company pays the remainin expenses. Suppose you have a car insurance policy with a $900 deductible provision (per claim) for collisions. During a 2-year period, you file claims for $550 and $1325. The annuanl premium for the policy is $400. Determine how much you would pay with and without the insurance policy with policy $1775, w/o $2225...
SOS!! 16) Which of the following is a condition that must be met for the decertification...
SOS!! 16) Which of the following is a condition that must be met for the decertification of a union? a The union must have at least hundred members. b The union must have served as the official bargaining agent for the employees for at least 3 years. c A closed-shop agreement must have existed between the union and the employer. d No labor contract must currently be in force. 7) Question 7 (2 points) In the context of performance-appraisal methods,...
Problem 33.2ish. How many strings of fourteen lowercase English letters are there which (a) start with...
Problem 33.2ish. How many strings of fourteen lowercase English letters are there which (a) start with the letter x, if letters may be repeated? (b) contain the letter x at least once, if letters can be repeated? (c) contain each of the letters x and y at least once, if letters can be repeated? (d) which contain at least one vowel, where letters may not be repeated?
Problem 2 A manager must decide how many machines of a certain type to buy. The...
Problem 2 A manager must decide how many machines of a certain type to buy. The machines will be used to manufacture a new gear for which there is increased demand. The manager has narrowed the decision to two alternatives: buy one machine or buy two. If only one machine is purchased and demand is more than it can handle, a second machine can be purchased at a later time. However, the cost per machine would be lower if the...
How many ml of both 75% and 5% stock must be combined to prepare 16 ounces...
How many ml of both 75% and 5% stock must be combined to prepare 16 ounces of a 25% product? Answer: [a] ml of 75% stock (#ml) Round to the nearest whole number Answer: [b] ml of 5% stock (#ml)  Round to the nearest whole number
which of the following statements is true? - A separate form 8949 must be filed for...
which of the following statements is true? - A separate form 8949 must be filed for each transaction for which the tax payer did not receive a form 1099B. - any taxpayer must file a separate schedule D for each form 1099B transaction with bases reported to the IRS. - short term transactions are reported on form 8949 and long-term transactions are reported on schedule D. - The totals from each schedule D are combined on form 8949.
A manager must decide how many machines of a certain type to purchase. Each machine can...
A manager must decide how many machines of a certain type to purchase. Each machine can process 101 customers per day. One machine will result in a fixed cost of $2,038 per day, while two machines will result in a fixed cost of $3,836 per day. Variable cost will be $22 per customer and revenue will be $49 per customer. Determine the break-even point in units for TWO machines. *Round your answers to 3 decimal places in your calculation if...
Which of these is not true of perfectly competitive markets? There must be many buyers and...
Which of these is not true of perfectly competitive markets? There must be many buyers and sellers Firms must produce a standardised product Firms are able to choose the price they charge The market must allow free entry and exit from the industry Which of these is not true of perfectly competitive markets? There must be many buyers and sellers Firms must produce a standardised product Firms are able to choose the price they charge The market must allow free...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT