Question

2. Suppose you have the 26 letters of the English alphabet on separate cards in a hat. You pick a card, write down the letter on the card, put the card back in the hat, mix up the cards, pick out another card, and so on. a) Write an expression for the probability that on your first six draws your letters spell JOKING.

Answer 1

b) Just as in part a) you create a six-letter “word.” (The six letters may or may not make an actual English word.) Now in the same way you create another six-letter “word,” and you do this 100,000 times. Write an expression for the probability that at least one of these 100,000 six-letter “words” will be JOKING.

Answer 2

This is sampling with replacement. The probability of drawing any of the 26 letters is 1/26 on each draw. The probability that on your first six draws your letters spell JOKING is\[(\frac{1}{26})^{6}\]

Answer 3

@kropot72 thank you. what is b: Write an expression for the probability that at least one of these 100,000 six-letter “words” will be JOKING?

Answer 4

1/100000? @kropot72

Answer 5

The number of permutations of the 26 letters taken 6 at a time without repetitions is
\[\frac{26!}{(26-6)!}=165,765,600\]
The probability of getting repeated words in 100,000 selections of words is obviously very small. In that case we can regard the drawing of each 6 letter word as a mutually exclusive event and the the probability that at least one of the 100,000 six-letter “words” will be JOKING is
\[100,000\times (\frac{1}{26})^{6}\]

Answer 6

Thanks. you are a saint!

Answer 7

You're welcome :)