In a box there are 9 balls, of which there are two white, three green and four black
1. Calculate the probability of:
(a) Choose a white ball
(b) Choose a green ball
2. (Conditional probability) If when taking two balls one followed by the other (without substituting), calculate the
probability of taking:
(a) one white and one black
(b) one green, one black and one white
3. (Independent events) If when taking two balls one followed by the other (substituting the first),
calculate the probability of taking:
(a) one white and one black
(b) one green and one white
4. Suppose an experiment in which two dice are rolled. Calculate the probability that the sum of
them as a result:
(a) Two points
(b) six points
5. In how many ways can 2 white, 4 red and 3 blue balls be arranged if:
(a) Being marked and in any order.
(b) Being marked, they want to accommodate leaving the same color together.
(c) No marks and you want to leave the same color together.
6. (Bayes theorem) Three machines M1, M2, M3 produce 50%, 30%, 20% of the total number of
products of a company. The percentages of items in poor condition for each machine are 5%,
2% and 3% respectively. If an item is selected at random, calculate:
(a) The probability that an item is defective.
(b) The probability that the defective item is produced by the first machine.
(c) The probability that the defective item is produced by the second machine.