A worker randomly places fruit in baskets. Of the 8 pieces of fruit, 6 are pears. The worker randomly selects 4 pieces of fruit for a basket. What is the probability that all 4 pieces selected are pears?

Rationale

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

To find the probability of selecting 4 pears out of 8 fruits (6 of which are pears), we can use the combination formula to determine the number of successful outcomes over the total possible outcomes. The successful selection of 4 pears from 6 can be calculated, resulting in a probability of 14-Mar.

A (02-Jan) YOUR ANSWER

This option suggests a very low probability that does not accurately reflect the selection of pears. The probability calculation involves combinations and this fraction does not correspond to any valid outcome in this scenario.

B (03-Feb) YOUR ANSWER

Similar to option A, this choice indicates a probability that does not align with the correct calculations. The probability of selecting 4 pears from 6 must be expressed in terms of combinations, and this option fails to represent that concept correctly.

C (04-Jan) YOUR ANSWER

This selection also underestimates the probability of choosing 4 pears from the available selections. The correct probability is derived from the combination of choosing pears and does not support this numerical representation, which does not stem from valid combinatorial logic.

D (14-Mar) CORRECT

This is the correct answer as it reflects the calculated probability of successfully selecting all 4 pieces as pears. By evaluating the combinations of pears (6 choose 4) and the total combinations of fruits (8 choose 4), it becomes evident that this result accurately represents the probability of the event occurring.

Conclusion

The probability of selecting 4 pears out of 6 available pears from a total of 8 fruits is calculated using combination theory, yielding the correct answer of 14-Mar. The other choices do not stem from the appropriate probabilistic calculations and thus fail to represent the actual likelihood of the event. Understanding combinations is crucial in determining probabilities in scenarios involving selections from distinct groups.

A worker randomly places fruit in baskets. Of the 8 pieces of fruit, 6 are pears. The worker randomly selects 4 pieces of fruit for a basket. What is the probability that all 4 pieces selected are pears?

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

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