Question

8.16 A traditional test for extrasensory perception (ESP)

Answer 1

Using probability of independent events, it is found that the probabilities are:

• a) $P(C) = \frac{1}{5}$

• b) $P(CI) = \frac{4}{25}$

• c) $P(C) = \frac{1}{125}$

• d) $P(C) = \frac{64}{125}$

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:

$P(C) = \frac{1}{5}$

And the probability of an incorrect guess is:

$P(I) = \frac{4}{5}$

Item a:

$P(C) = \frac{1}{5}$

Item b:

C and I are independent events, hence:

$P(CI) = P(C)P(I) = \frac{1}{5} \times \frac{4}{5} = \frac{4}{25}$

Item c:

$P(CCC) = \left(\frac{1}{5}\right)^3 = \frac{1}{125}$

Item d:

$P(III) = \left(\frac{4}{5}\right)^3 = \frac{64}{125}$

You can learn more about independent events at brainly.com/question/21763634