Question 23

The probability that all 4 pieces selected are pears is 14-Mar.

To determine the probability that all 4 pieces selected are pears, we can use combinations to calculate the number of favorable outcomes over the total outcomes. The probability is calculated as the ratio of choosing 4 pears from 6 pears out of a total of 8 fruits.

A) 02-Jan

This option suggests a probability of 0.02, which is incorrect. Given the context, the number of ways to choose 4 pears from 6 is significantly higher than this option indicates, making it an insufficient representation of the actual probability.

B) 03-Feb

The probability represented by this option implies a ratio of 0.03, which does not accurately reflect the situation. The actual probability of selecting all pears is determined through the combination formula, and 0.03 is too low considering the favorable outcomes available.

C) 04-Jan

This option presents a probability of 0.04, which is also incorrect. While it is a higher value than the previous options, it still underestimates the likelihood of selecting all pears, given that the actual calculation yields a higher probability through proper combinatorial analysis.

D) 14-Mar

This option signifies the correct probability of selecting all 4 pieces as pears. The calculation involves determining the number of ways to choose 4 pears from 6 (which is 15) over the total ways to choose any 4 fruits from 8 (which is 70). Thus, the probability is 15/70, simplifying to 3/14, or approximately 0.214, aligning with the representation of 14-Mar.

Conclusion

The correct answer, 14-Mar, accurately represents the probability of selecting 4 pears among the total fruit available. All other options fall short of this calculation, either by underestimating the total combinations or by providing incorrect numerical values, thus confirming that D is the only valid choice based on the provided scenario.