Question

Question *
Every visitor in a public library has to either choose a book or use a computer,
70% of these visitors use the computer. Out of those who use the computer, 45%
do a research. Out of the visitors who choose a book, 80% do a research. We
meet, at random, one of the visitors in this library. If the visitor did a research, the
probability that he used the computer is:
0.4324
0.5675
None of these
0.8651

Answer 1

Using conditional probability, it is found that there is a 0.5675 = 56.75% probability that he used the computer.

Conditional Probability

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

• P(B|A) is the probability of event B happening, given that A happened.
• $P(A \cap B)$ is the probability of both A and B happening.
• P(A) is the probability of A happening.

In this problem:

• Event A: Did a research.
• Event B: Used a computer.

For making a research, there are two cases:

• 45% of 70%(using a computer).
• 80% of 100 - 70 = 30%(using a book).

Then:

$P(A) = 0.45(0.70) + 0.8(0.30) = 0.555$

The probability of doing a research and using a computer is 45% of 70%, thus:

$P(A \cap B) = 0.45(0.7)$

Then, the conditional probability is:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.45(0.7)}{0.555} = 0.5675$

0.5675 = 56.75% probability that he used the computer.

A similar problem is given at https://brainly.com/question/14398287