Question

hello thanks for viewing my question I seem to be having some difficulty on this can you please help me thank you

Answer 1

ANSWER

0.306 or 30.6%

EXPLANATION

Note: Probability is the number of desired results divided by the total number of results.

Combination formula to apply:

$C_{n,r}\text{ = }\frac{n!}{r!(n-r)!}$

Desired Results:

3 brown worms from 7

4 red worms from 6

$\begin{gathered} Desired\text{ Result = C}_{7,3}\times C_{6,4} \\ \text{ = }\frac{7!}{3!(7-3)!}\times\frac{6!}{4!(6-4)!} \\ \text{ = 35}\times15 \\ \text{ = 525} \end{gathered}$

Total Result:

$\begin{gathered} Total\text{ Result = C}_{13,7} \\ \text{ = }\frac{13!}{7!(13-7)!} \\ \text{ = 1716} \end{gathered}$

Determine the Probability

$\begin{gathered} Probability\text{ = }\frac{Desired\text{ outcome}}{total\text{ outcome}} \\ \text{ = }\frac{525}{1716} \\ \text{ = 0.3059} \\ \text{ = 0.306 or 30.6\%} \end{gathered}$

Hence, the probability that she will choose 3 brown worms and 4 red worms is 0.306 or 30.6%.