i have my final tomorrow and this question was on my review? im having trouble with probability so...
"your cat walks over the computer keyboard while you're away and hits three random letters. what is the probability that the word RAT appears"
So on my calculator do i 26 nCr 3
how would i solve this?
To solve this probability question, you need to determine the number of favorable outcomes (the number of ways the word "RAT" can be formed) and the total number of possible outcomes (the total number of ways three random letters can be selected).
To find the number of favorable outcomes, you need to consider that the word "RAT" can only be formed if the cat chooses the letter "R," followed by "A," and then "T." Since each letter is chosen randomly, the chance of each letter being selected is independent. Therefore, the probability of selecting "R" is 1/26, the probability of selecting "A" after selecting "R" is 1/26, and the probability of selecting "T" after selecting "A" is also 1/26.
To find the total number of possible outcomes, you need to consider that each letter can be any one of the 26 letters of the English alphabet. Since the cat chooses three random letters, there are 26 choices for the first letter, 26 choices for the second letter, and 26 choices for the third letter. Therefore, the total number of possible outcomes is 26 × 26 × 26 = 26^3.
To calculate the probability, divide the number of favorable outcomes by the total number of possible outcomes. In this case, the probability can be calculated as:
(1/26) × (1/26) × (1/26) / (26^3)
Simplifying this expression, you have:
1 / (26 × 26 × 26)
And further reducing it:
1 / 17576
So, the probability that the word "RAT" appears when the cat types three random letters is 1/17576.
Regarding your calculator calculation, using "26 nCr 3" calculates the number of combinations (not permutations) of choosing 3 letters from the 26 available (order doesn't matter). While combinations are useful in some cases, in this problem, we need permutations (since the order of the letters matters). Therefore, calculating combinations is not appropriate for solving this particular question.