Use the numbers given in step 8 to find the probability in step 9. ## Step 8Refer to the formula below for the probability of exactly $ k $ successes in a random sample of size $ n $.\[P(X = k) = \frac{{C_M^k \cdot C_{N-M}^{n-k}}}{C_N^n}\]Recall that $ P(X = k) $, the probability of $ k $ successes, is written $ P(X = k) $. The number of successes for $ P(X = 2) $ is $ k = 2 $. The number of successes for $ P(X = 3) $ is $ k = 3 $. Since we are given that four plants emerged, we have $ n = 4 $.## Step 9Refer to the formula below.\[P(X = k) = \frac{{C_M^k \cdot C_{N-M}^{n-k}}}{C_N^n}\]We have determined $ N = 12 $, $ M = 6 $, $ n = 4 $, and $ k = 2 $ for $ P(X = 2) $ and $ k = 3 $ for $ P(X = 3) $. The remaining values needed are $ N - M $ and $ n - k $.Substitute the values from the previous step into the hypergeometric probability formula, or use technology. Round your final answer to four decimal places.\[P(2 \leq X \leq 3) = P(X = 2) + P(X = 3)\]\[= \frac{C_6^2 \cdot C_6^2}{C_{12}^4} + \frac{C_6^3 \cdot C_6^1}{C_{12}^4}\]Therefore, the probability that two or three plants emerged from treated seeds is $\_\_\_\_\_\_.$

The formula for hypergeometric distribution is given below.Given that,The formula for Hypergeometric…

Answered: Therefore, the probability that two or…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Use the numbers given in step 8 to find the probability in step 9.

## Step 8

Refer to the formula below for the probability of exactly $ k $ successes in a random sample of size $ n $.

\[
P(X = k) = \frac{{C_M^k \cdot C_{N-M}^{n-k}}}{C_N^n}
\]

Recall that $ P(X = k) $, the probability of $ k $ successes, is written $ P(X = k) $. The number of successes for $ P(X = 2) $ is $ k = 2 $. The number of successes for $ P(X = 3) $ is $ k = 3 $. Since we are given that four plants emerged, we have $ n = 4 $.

## Step 9

Refer to the formula below.

\[
P(X = k) = \frac{{C_M^k \cdot C_{N-M}^{n-k}}}{C_N^n}
\]

We have determined $ N = 12 $, $ M = 6 $, $ n = 4 $, and $ k = 2 $ for $ P(X = 2) $ and $ k = 3 $ for $ P(X = 3) $. The remaining values needed are $ N - M $ and $ n - k $.

Substitute the values from the previous step into the hypergeometric probability formula, or use technology. Round your final answer to four decimal places.

\[
P(2 \leq X \leq 3) = P(X = 2) + P(X = 3)
\]

\[
= \frac{C_6^2 \cdot C_6^2}{C_{12}^4} + \frac{C_6^3 \cdot C_6^1}{C_{12}^4}
\]

Therefore, the probability that two or three plants emerged from treated seeds is $\_\_\_\_\_\_.$

Expert Solution

Step 1: Determine the given data in the question

The formula for hypergeometric distribution is given below.

Given that,

$N equals 12 M equals 6 n equals 4$

The formula for Hypergeometric distribution is,

$P left parenthesis x equals k right parenthesis equals fraction numerator M subscript C subscript k end subscript space N minus M subscript C subscript n minus k end subscript end subscript over denominator N subscript C subscript n end subscript end fraction equals fraction numerator 6 subscript C subscript k end subscript space 12 minus 6 subscript C subscript 4 minus k end subscript end subscript over denominator 12 subscript C subscript 4 end subscript end fraction 12 subscript C subscript 4 end subscript equals fraction numerator 12 factorial over denominator 4 factorial left parenthesis 12 minus 4 right parenthesis factorial end fraction equals 495 P left parenthesis X equals k right parenthesis equals fraction numerator 6 subscript C subscript k end subscript space 12 minus 6 subscript C subscript 4 minus k end subscript end subscript over denominator 495 end fraction$