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8.16 A traditional test for extrasensory perception (ESP)
involves a set of playing cards, each of which shows a different
symbol (circle, square, cross, star, or wavy lines). If C
represents a correct guess and I an incorrect guess, what is the
probability of
a. C?
b. CI (in that order) for two guesses?
c. CCC for three guesses?
d. III for three guesses?

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