Respuesta :
Answer:
0.113 = 11.3% probability that she will choose 8 brown worms and 4 red worms
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, we order in which the worms are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
8 brown worms, from a set of 10.
4 red worms, from a set of 9.
So
[tex]D = C_{10,8}*C_{9,4} = \frac{10!}{8!(10-8)!}*\frac{9!}{4!(9-4)!} = 5670[/tex]
Total outcomes:
12 worms from a set of 10 + 9 = 19. So
[tex]T = C_{19,12} = \frac{19!}{12!(19-12)!} = 50388[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{5670}{50388} = 0.113[/tex]
0.113 = 11.3% probability that she will choose 8 brown worms and 4 red worms
