Question

question 13

a pile of cards contains eight cards, numbered 1 through 8.
what is the probability of not choosing the 6?

• \\(\frac{1}{7}\\)
• \\(\frac{1}{8}\\)
• \\(\frac{7}{8}\\)
• \\(\frac{8}{7}\\)

Explanation:

Determine the total number of outcomes

The pile contains eight cards numbered 1 through 8.

$$ S = \{1, 2, 3, 4, 5, 6, 7, 8\} \implies n(S) = 8 $$

Identify the favorable outcomes

We want the probability of NOT choosing the 6. The favorable outcomes are all cards except 6.

$$ E = \{1, 2, 3, 4, 5, 7, 8\} \implies n(E) = 7 $$

Calculate the probability

The probability is the ratio of favorable outcomes to total outcomes.

$$ P(\text{NOT } 6) = \frac{n(E)}{n(S)} = \frac{7}{8} $$

Answer:

• (A) \(\frac{1}{7}\)
• (B) \(\frac{1}{8}\)
• (C) \(\frac{7}{8}\) (Correct answer)
• (D) \(\frac{8}{7}\)