Each of the first 6 letters of the alphabet is printed on a separate card. The...

Each of the first 6 letters of the alphabet is printed on a separate card. The letter “a” is printed twice. What is the probability of drawing 4 cards and getting the letters f, a, d, a in that order? Same question if the order does not matter.

Expert Solution

We have total 7 cards: 6 cards for each letter and one more card for letter a.

Out of 7 cards, 1 card is f so probability of letter f card at first draw is 1/7.

After that out of remaining 6 cards, 2 cards are letter a so probability of getting letter a card in second draw is 2/6.

After that out of remaining 5 cards, 1 card is letter d so probability of getting letter d card in third draw is 1/5.

After that out of remaining 4 cards, 1 card is letter a so probability of getting letter a card in fourth draw is 1/4.

Therefore the probability of drawing 4 cards and getting the letters f, a, d, a in that order is

(1/7) * (2/6) * (1/5) * (1/4) = 0.0024

-------------------------

Now order of cards is not important so we can use combination.

Number of ways of selecting 4 cards out of 7 is C(7,4) = 35.

Number of ways of selecting 2 letter a cards, 1 letter f cards and 1 letter d card is

C(2,2) * C(1,1) * C(1,1) = 1

The required probability is

1 / 35 = 0.0286

milcah answered 1 month ago

The English alphabet has 26 letters. There are 6 vowels. (a, e, i, o, u, and...

The English alphabet has 26 letters. There are 6 vowels. (a, e, i, o, u, and sometimes y). Suppose we randomly select 8 letters from the alphabet without replacement. Let X = the number of vowels chosen (including y as a vowel). a. How many possible ways are there to select the 8 out of 26 letters (order does not matter) without replacement? b. What is the probability that X = 2 c. What is the probability that X=1? d....

6. Passwords are composed from lower- and uppercase letters of the English alphabet,digits and 34 special...

6. Passwords are composed from lower- and uppercase letters of the English alphabet,digits and 34 special characters. What is the exponential generating function of the sequence an=number of passwords with at least one capital letter, one number and one special character.

In the game of ScrabbleTM, the letters of the English alphabet are inscribed on tiles

In the game of ScrabbleTM, the letters of the English alphabet are inscribed on tiles and a prescribed number of tiles are provided for each letter. Consider an ensemble of ScrabbleTM tiles with a probability distribution defined by the frequency of tiles in the box. Explain how to calculate the information entropy of this ensemble. It is not necessary to actually Compute the entropy, but you can if you wish.

Suppose you want to form words with 3 letters and all letters in the alphabet can...

Suppose you want to form words with 3 letters and all letters in the alphabet can be used except A and B (so, XYZ would be a word for example even though it does not make sense). a) How many possibilities do you have if repetition is permitted and ordering is relevant, how many possibilities do you have if repetition is not permitted and ordering is relevant; how many possibilities do you have if repetition is not permitted and ordering...

Alphabet Company, which uses the periodic inventory method, purchases different letters for resale. Alphabet had no...

Alphabet Company, which uses the periodic inventory method, purchases different letters for resale. Alphabet had no beginning inventory. It purchased A thru G in January at $4 per letter. In February, it purchased H thru L at $6 per letter. It purchased M thru R in March at $7 per letter. It sold A, D, E, H, J and N in October. There were no additional purchases or sales during the remainder of the year. If Alphabet Company uses the...

A Caesar cipher encrypts a message by shifting letters in the alphabet. For example, a shift...

A Caesar cipher encrypts a message by shifting letters in the alphabet. For example, a shift of 4 maps 'a' to 'e' and maps 'p' to 't' Here is a famous line from Shakespeare encrypted with a shift of 4: 'vq dg qt pqv vq dg: vjcv ku vjg swguvkqp.' (a) Write a program that takes as input a string to be encrypted and an integer encrpytion shift (such as 4 mentioned earlier), and prints the encrypted string. [Hint: zip()...

9. The Central Intelligence Agency has specialists who analyze the frequencies of letters of the alphabet...

9. The Central Intelligence Agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages that are sent as ciphered text. In standard English text, the letter r is used at a rate of 6%. a. Find the mean and standard deviation for the number of times the letter r will be found on a typical page of 2600 characters. (1 dp) b. In an intercepted ciphered message sent to Iran, a...

Write a C++ function that lets the user enter alphabet letters into a static char array...

Write a C++ function that lets the user enter alphabet letters into a static char array until either the user enters a non-alphabet letter or, it has reached the MAXSIZE. You can use the isalpha([Char]) function to check if the input is an alphabet letter or not. void fillArray (char ar[], size_t& size){ // this is the function prototype }

A person has to create a code. The code must contain exactly 6 letters. The first...

A person has to create a code. The code must contain exactly 6 letters. The first letter must be a vowel that is not an E or I. The second letter must be either a J, K, or L. The third letter must be a consonant that is not a G or R. The fourth letter must be a vowel that is not an I. The fifth letter must be a consonant. If repetition of letters are not allowed, how...

4. The Hawaiian alphabet has twelve letters: five vowels (a, e, i, o, and u) and...

4. The Hawaiian alphabet has twelve letters: five vowels (a, e, i, o, and u) and seven consonants (h, k, l, m, n, p, and w). For the purpose of this exercise we will define an n–letter “word” as an ordered collection of n of these twelve letters with repeats allowed. Obviously, most such “words” will be nonsense words. a) How many possible four–letter Hawaiian “words” are there? b) What is the probability a randomly selected four–letter “word” has no...

Question