A botanist conducted an experiment to study the germination rates of seeds in two different soil mixtures, Mixture A and Mixture B. The results of the experiment are partially shown in the table below, where is a positive constant.
| Soil Mixture | Germinated | Did Not Germinate |
|---|---|---|
| Mixture A | ||
| Mixture B |
Of the seeds in the experiment that did not germinate, the probability that the seed was planted in Mixture A is . Given that a seed selected at random from the experiment germinated, what is the probability that it was planted in Mixture A?
Cevap: 0.375
Cevap
3/8 (or 0.375)
To find the probability that a germinated seed was planted in Mixture A, we must first solve for the variable . The number of seeds in Mixture A that did not germinate is , and the total number of seeds that did not germinate is . We are given that the probability a non-germinated seed was planted in Mixture A is . Setting up the equation: yields , so . Substituting this value back into the table, the number of germinated seeds in Mixture A is . The total number of germinated seeds is the sum of germinated seeds in Mixture A and Mixture B: . Thus, the probability that a germinated seed was planted in Mixture A is , which simplifies to (or ).
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Anahtar Kavram
Conditional Probability in Two-Way Tables