To determine which suit has the experimental probability closest to the theoretical probability, let's go through the process step-by-step.
1. Theoretical Probability Calculation:
- In a standard deck of playing cards, there are 4 suits: Clubs, Diamonds, Hearts, and Spades.
- Each suit has an equal probability of being selected, which is [tex]\( \frac{1}{4} = 0.25 \)[/tex] or 25%.
2. Experimental Probabilities Calculation:
- The total number of experiments (card selections) is 50.
- The frequency of each suit being selected is given in the table.
We calculate the experimental probability for each suit by dividing the frequency of the suit by the total number of experiments.
- Clubs: [tex]\( \frac{12}{50} = 0.24 \)[/tex]
- Diamonds: [tex]\( \frac{4}{50} = 0.08 \)[/tex]
- Hearts: [tex]\( \frac{25}{50} = 0.50 \)[/tex]
- Spades: [tex]\( \frac{9}{50} = 0.18 \)[/tex]
3. Comparison of Experimental Probabilities to Theoretical Probability:
- Theoretical probability: [tex]\( 0.25 \)[/tex]
Differences between experimental and theoretical probabilities:
- Clubs: [tex]\( |0.24 - 0.25| = 0.01 \)[/tex]
- Diamonds: [tex]\( |0.08 - 0.25| = 0.17 \)[/tex]
- Hearts: [tex]\( |0.50 - 0.25| = 0.25 \)[/tex]
- Spades: [tex]\( |0.18 - 0.25| = 0.07 \)[/tex]
4. Conclusion:
- We observe that the absolute differences from the theoretical probability are:
- Clubs: 0.01
- Diamonds: 0.17
- Hearts: 0.25
- Spades: 0.07
The smallest difference is for Clubs, with a difference of 0.01.
Therefore, the suit for which the experimental probability is closest to the theoretical probability is Clubs (A).
