What is the probability of choosing a diamond or a queen in a standard deck of cards?(1 point)

Responses

1352+452−151
Start Fraction 13 over 52 End Fraction plus Start Fraction 4 over 52 End Fraction minus Start Fraction 1 over 51 End Fraction

1352+452+152
Start Fraction 13 over 52 End Fraction plus Start Fraction 4 over 52 End Fraction plus Start Fraction 1 over 52 End Fraction

1352+451−152
Start Fraction 13 over 52 End Fraction plus Start Fraction 4 over 51 End Fraction minus Start Fraction 1 over 52 End Fraction

1352+452−152

1 answer

To find the probability of choosing a diamond or a queen in a standard deck of 52 cards, we can calculate it as follows:

  1. Number of Diamonds: There are 13 diamonds in a deck.
  2. Number of Queens: There are 4 queens in a deck.
  3. Overlap: Since one of the queens is a diamond (the queen of diamonds), we need to account for this overlap.

Using the principle of inclusion-exclusion, the probability \( P \) can be calculated as:

\[ P(\text{diamond or queen}) = P(\text{diamond}) + P(\text{queen}) - P(\text{queen of diamonds}) \]

Calculating these probabilities:

  • \( P(\text{diamond}) = \frac{13}{52} \)
  • \( P(\text{queen}) = \frac{4}{52} \)
  • \( P(\text{queen of diamonds}) = \frac{1}{52} \)

Putting it all together:

\[ P(\text{diamond or queen}) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{13 + 4 - 1}{52} = \frac{16}{52} = \frac{4}{13} \]

So the correct approach would be:

\[ \frac{13}{52} + \frac{4}{52} - \frac{1}{52} \]

Looking at the options you provided, the one that matches this calculation is:

1352 + 452 - 151

Thus, the probability of choosing a diamond or a queen in a standard deck of cards is best represented by this formula.