Question

a tv remote has keys for channels 0–9. you select one key at random.

1. what is the probability that you select channel 6?
2. what is the probability that you select a channel that is an odd number?
3. what is the probability that you select a channel less than 8?
4. what is the probability that you don’t select 1?

a multiple - choice test has six possible answers for each question.

1. if you guess at an answer, what is the probability that you select the correct answer for one particular question?
2. if you guess at an answer, what is the probability that you select the incorrect answer for one particular question?
3. if you correctly eliminate two of the six possible answers and guess from the remaining possibilities, what is the probability that you select the correct answer to that question?
4. if you correctly eliminate two of the six possible answers and guess from the remaining possibilities, what is the probability that you select the incorrect answer to the problem?

Explanation:

43.

Step1: Determine total outcomes

Total channels (keys) are 0 - 9, so total outcomes \( n = 10 \).

Step2: Determine favorable outcomes

Favorable outcome (selecting 6) is \( m = 1 \).

Step3: Calculate probability

Probability \( P=\frac{m}{n}=\frac{1}{10} \).

Step1: Determine total outcomes

Total channels (keys) are 0 - 9, so total outcomes \( n = 10 \).

Step2: Determine favorable outcomes

Odd numbers in 0 - 9: 1, 3, 5, 7, 9. So \( m = 5 \).

Step3: Calculate probability

Probability \( P=\frac{m}{n}=\frac{5}{10}=\frac{1}{2} \).

Step1: Determine total outcomes

Total channels (keys) are 0 - 9, so total outcomes \( n = 10 \).

Step2: Determine favorable outcomes

Numbers less than 8: 0, 1, 2, 3, 4, 5, 6, 7. So \( m = 8 \).

Step3: Calculate probability

Probability \( P=\frac{m}{n}=\frac{8}{10}=\frac{4}{5} \).

Answer:

\(\frac{1}{10}\)

44.