Questions: When using the square always be careful to avoid double-counting outcomes. multiplication rule odds formula addition rule polygraph test

Solution Steps

The question seems to be asking about a rule in probability or combinatorics that requires caution to avoid double-counting outcomes. The most common rule associated with this caution is the "addition rule," which is used when calculating the probability of the union of two events.

We need to calculate the probability of drawing either a heart or a queen from a standard deck of 52 playing cards. This involves using the addition rule in probability to account for the overlap between the two events.

• The probability of drawing a heart, \( P(\text{Heart}) \), is calculated as the number of hearts divided by the total number of cards: \[ P(\text{Heart}) = \frac{13}{52} = 0.25 \]

• The probability of drawing a queen, \( P(\text{Queen}) \), is calculated as the number of queens divided by the total number of cards: \[ P(\text{Queen}) = \frac{4}{52} \approx 0.07692 \]

• The probability of drawing a queen of hearts, \( P(\text{Queen of Hearts}) \), is calculated as the number of queen of hearts divided by the total number of cards: \[ P(\text{Queen of Hearts}) = \frac{1}{52} \approx 0.01923 \]

Using the addition rule for probability, we find the probability of drawing a heart or a queen: \[ P(\text{Heart or Queen}) = P(\text{Heart}) + P(\text{Queen}) - P(\text{Queen of Hearts}) \] Substituting the values: \[ P(\text{Heart or Queen}) = 0.25 + 0.07692 - 0.01923 \approx 0.3077 \]

Final Answer