To determine the probability of choosing a specific secret code, such as the code "7Q", you need to understand the concept of independent events in probability.
Here, choosing a letter from the alphabet and choosing a digit from 0 to 9 are two independent actions.
1. Understanding the Problem:
- We need to find the probability of selecting the digit '7' and the letter 'Q'.
2. Probabilities of Individual Events:
- There are 26 letters in the alphabet. The probability of choosing the letter 'Q' is therefore:
[tex]\[
P(Q) = \frac{1}{26}
\][/tex]
- There are 10 digits (from 0 to 9). The probability of choosing the digit '7' is:
[tex]\[
P(7) = \frac{1}{10}
\][/tex]
3. Combined Probability for Independent Events:
- Since choosing a letter and choosing a digit are independent events (one does not affect the other), we use the multiplication rule for independent events. This rule states that the probability of both events occurring together (denoted as [tex]\( P(7 \cap Q) \)[/tex]) is the product of their individual probabilities:
[tex]\[
P(7 \cap Q) = P(7) \times P(Q)
\][/tex]
Given this understanding, the correct equation that represents the probability of choosing the secret code "7Q" is:
[tex]\[
P(7 \cap Q) = P(7) \times P(Q)
\][/tex]
Among the provided options, this corresponds to:
[tex]\[
P(7 \cap Q) = P(7) \times P(Q)
\][/tex]
Thus, the correct answer is:
[tex]\[
P(7 \cap Q)=P(7) \times P(Q)
\][/tex]
Based on this equation and the known probabilities, the result calculated through the given Python solution is:
[tex]\[
P(7 \cap Q) = \frac{1}{10} \times \frac{1}{26} = 0.0038461538461538464
\][/tex]
Therefore, the probability of choosing the secret code "7Q" is approximately [tex]\( 0.0038 \)[/tex] or [tex]\( 0.3846\% \)[/tex].
