Respuesta :
Answer:
As a simplified fraction, the probability that the first randomly taken candy will be red and second will be red again is [tex]\frac{2}{9}[/tex]
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the candies are selected 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:
2 candies from a set of 5. So
[tex]D = C_{5,2} = \frac{5!}{2!(5-2)!} = 10[/tex]
Total outcomes:
2 candies from a set of 10. So
[tex]T = C_{10,2} = \frac{10!}{2!(10-2)!} = 45[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{10}{45} = \frac{2}{9}[/tex]
As a simplified fraction, the probability that the first randomly taken candy will be red and second will be red again is [tex]\frac{2}{9}[/tex]
