Question
A box contains 7 letters, shown as CHARTED. What is the probability of the outcome RAT in that order if 3 letters are drawn one by one (a) with replacement? (b) without replacement? The probability of the outcome RAT in that order if 3 letters are drawn with replacement is (Type your answer as a fraction.)
Ask by Medina Cole. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability of drawing RAT in order with replacement is 1/343.
Solution
We have 7 letters in the box (C, H, A, R, T, E, D), and each letter is equally likely to be chosen.
For drawing with replacement:
• The probability of drawing "R" on the first draw is 1/7.
• The probability of drawing "A" on the second draw is 1/7.
• The probability of drawing "T" on the third draw is 1/7.
Since the draws are independent, multiply the probabilities:
(1/7) × (1/7) × (1/7) = 1/343
Thus, the probability of the outcome RAT in that order when drawing 3 letters with replacement is 1/343.
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Simplify this solution Mind Expander
When drawing with replacement, the probability of getting each letter is independent. There are 7 letters in total, so the probability of drawing 'R' first is 1/7, 'A' second is also 1/7, and 'T' third is again 1/7. Therefore, the probability of the outcome "RAT" in that order is: (1/7) * (1/7) * (1/7) = 1/343. Now, for without replacement, when you draw 'R' first, you remove it from the box, leaving 6 letters. So the probability for 'R' is again 1/7, but then 'A' will have a probability of 1/6 now, and 'T' will be 1/5 on the third draw. Hence, the probability of "RAT" in that order without replacement is: (1/7) * (1/6) * (1/5) = 1/210.
