The analysis of results from a leaf transmutation experiment (turning a leaf int

Question

The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by type of transformation completed: A naturalist randomly selects three leaves from this set, without replacement. Determine the following probabilities. (N = 300) (a) Exactly one has undergone both types of transformations. (b) At least one has undergone both transformations. (c) Exactly one has undergone one but not both transformations. (d) At least one has undergone at least one transformation. (e) Determine the mean and variance of the selected three leaves that undergone both types of transformations.

Explanation / Answer

a) exactly one has undergone both types of transformation means , 243 instances are for both types of trnasformations

exactly 1 means , yes , no , no for transformation so

243/300 * 57/299 * 56/298

as 300-243 = 57 cases where both transaformations did not occur. as the selection is without replacement the number of leaves in the total selection reduces

b)

at least 1 can be calculated as 1 - None or P1 +p2 +p3 leaves

1 - 57/300=0.81

c)

total number of cases for one but not both are

26+13 = 39

so the probability is

39/300 * 261/299 * 260/298

d)

total number of cases for atleast 1 transaformations are

243 + 26 + 13 = 282

so

yes no no + yes yes no + yes yes yes

282/300 * 18/299* 17/298 + 282*281*18/(300*299*298) + 282/300 * 281/299 * 280/298

Please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines   

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.