Solved: The analysis of results from a leaf transmutation

Step 1 of 4

Given the leaf transformation experiment table is given below.

\(\begin{array}{|lccc|} \hline & & {\begin{array}{c} \text { Total Textural } \\ \text { Transformation } \end{array}} \\ \hline & & \text { Yes } & \text { No } \\ \text { Total Color } & \text { Yes } & 243 & 26 \\ \text { Transformation } & \text { No } & 13 & 18 \\ \hline \end{array}\)

Here, N, n and K is

\(\mathrm{N}=243+26+13+18=300\)

The sample size n is randomly selected.

So n= 3.

K= 243 (both type of transformations)

Then the probability mass function is

\(\mathrm{P}(\mathrm{X}=\mathrm{x})=\frac{\left(\begin{array}{l} K \\ 2 \end{array}\right)\left(\begin{array}{c} N-K \\ n-x^{\prime} \end{array}\right)}{\left(\begin{array}{l} N \\ n \end{array}\right)}\)

Where, N=300, n=3 and K=243.

Our goal is:

a). We need to find the probability that exactly one leaf has undergone both types of transformations.

b). We need to find the probability that at least one leaf has undergone both types of transformations.

c). We need to find the probability that exactly one has undergone one but not both transformations.

d). We need to find the probability that at least one has undergone at least one transformation.