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

orchestra answered 1 year ago

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