Respuesta :
Using probability of independent events, it is found that the probabilities are:
- a) [tex]P(C) = \frac{1}{5}[/tex]
- b) [tex]P(CI) = \frac{4}{25}[/tex]
- c) [tex]P(C) = \frac{1}{125}[/tex]
- d) [tex]P(C) = \frac{64}{125}[/tex]
Independent Events:
- For multiple independent events, the probability of all happening is the multiplication of the probability of each happening.
In this problem:
- One guess is taken from a set of 5 elements, hence the probability of a correct guess is:
[tex]P(C) = \frac{1}{5}[/tex]
And the probability of an incorrect guess is:
[tex]P(I) = \frac{4}{5}[/tex]
Item a:
[tex]P(C) = \frac{1}{5}[/tex]
Item b:
C and I are independent events, hence:
[tex]P(CI) = P(C)P(I) = \frac{1}{5} \times \frac{4}{5} = \frac{4}{25}[/tex]
Item c:
[tex]P(CCC) = \left(\frac{1}{5}\right)^3 = \frac{1}{125}[/tex]
Item d:
[tex]P(III) = \left(\frac{4}{5}\right)^3 = \frac{64}{125}[/tex]
You can learn more about independent events at https://brainly.com/question/21763634
