Question

4. Some scrabble letters are laid out that spell RECORDER. If they are all turned over and scrambled,

what is the probability that if you order them and then flip them back over that you will spell out
RECORDER again? List your answer in 3 ways. (4 marks total - 1 for sample space and 3 for work
below)
a) As a fraction
b) As a decimal
c) As a percent

Answer 1

The probability of reordering and flipping Scrabble letters to spell 'RECORDER' again is 1/10080 as a fraction, 0.000231 as a decimal, and 0.0231% as a percent.

Step-by-step explanation:

The question asks for the probability of reordering scrambled Scrabble letters to spell 'RECORDER'. There are 8! (eight-factorial) ways to arrange these 8 letters, which is our sample space. However, since the letter 'R' repeats 3 times and the letter 'E' repeats 2 times, we adjust the sample space by dividing by the factorial of these repetitions, resulting in a denominator of 8!/(3!2!). The desired outcome is only one specific arrangement of these letters, so there is only 1 favorable outcome. Hence, the probability as a fraction is 1/(8!/(3!2!)), as a decimal is approximately 0.000231, and as a percent is approximately 0.0231%.

a) Fraction: 1/10080

b) Decimal: 0.000231

c) Percent: 0.0231%

Answer 2

Answer: The answers are (a)1/8th (b) 0.125 (c) 12.5%

Step-by-step explanation:

How I drew this conclusion is, you have 8 letters in RECORDER so its 8/64 the same spot for every letter which simplifies to 1/8th. Now for the decimal divide 8 into 64 to get 0.125 decimal form. Lastly, for the percent 8 * 100 = 0.125 then 0.125 * 100 gets you 12.5%. Hope this helps you understand good luck.