Phillip is making a sign, and has cut the letters of the word THEATRETTE out of woodand placed them in his toolbox. If a letter is selected at random from the toolbox, thenthe probability that it is a T is单项选择题
A
a. 1/6
B
b. 1/5
C
c. 2/5
D
d. 3/10

Question

Phillip is making a sign, and has cut the letters of the word THEATRETTE out of woodand placed them in his toolbox. If a letter is selected at random from the toolbox, thenthe probability that it is a T is单项选择题

A

a. 1/6

B

b. 1/5

C

c. 2/5

D

d. 3/10

BlackTom AI · Accepted Answer

Probability = (number of favorable letters) / (total number of letters). This is the key concept: when selecting one item at random from equally likely outcomes, probability is the count of desired outcomes divided by the count of all possible outcomes.

1) Relevant knowledge points:
- Count each letter in the word to get the sample space size.
- Count how many of those letters are the desired letter (T).
- Reduce the resulting fraction to simplest form.

2) Step-by-step reasoning:
- Write the word and index each letter: T H E A T R E T T E.
- Count total letters: there are 10 letters in the word.
- Count the T’s: positions 1, 5, 8, and 9 are T’s, so there are 4 T’s.

3) Calculations with intermediate steps:
- Total outcomes = 10.
- Favorable outcomes (T) = 4.
- Probability = 4 / 10.
- Reduce the fraction: divide numerator and denominator by 2 → (4 ÷ 2) / (10 ÷ 2) = 2 / 5.

4) Why this answer is correct:
Because each letter cut from the sign is equally likely to be selected, the probability of selecting a T equals the fraction of letters that are T’s. With 4 out of 10 letters being T, the simplified probability 2/5 exactly represents that proportion.

5) Why the other choices are incorrect:
- a. 1/6 would correspond to 1.67 T’s per 10, which is not possible here (and is not 4/10).
- b. 1/5 equals 2/10, but we have 4 T’s, so it understates the probability.
- d. 3/10 equals 3 T’s out of 10, but we actually have 4 T’s, so it is too small.

6) Conclusion:
The correct probability is 4/10, which simplifies to 2/5. This matches the provided answer: c. 2/5.

Phillip is making a sign, and has cut the letters of the word THEATRETTE out of woodand placed them in his toolbox. If a letter is selected at random from the toolbox, thenthe probability that it is a T is单项选择题

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