1. Exercises (1) 1. A man has two kids. What’s the probability that both are girls, given that one of them is a girl

2. Exercises (2) Consider the experiment of drawing 2 cards without replacement from a deck of playing cards(52 cards). Show the tree diagram for this experience. Find 1. The probability that the first and the second cards are not face cards. 2. The probability that the second card is not a face card and the first is. 3. The probability that the second card is not a face card Show the tree diagram of the problem!

3. Exercises (3) 1. In the experiment of tossing a coin twice. Let E be the event that the outcome of the first toss is tail and let F be the event that the outcome is head in the second toss Show that E & F are independent. 2. Assume that E & F & G are independent events and p(E)=0.22, p(F) = 0.5 and p(G) = 0.3. Find: P(E ∩ F), p(E ∩ F ∩ G)

4. Exercises (4) The radio of a car is manufactured in three different locations (Plants A, B and C) before sent for final assembly. The table on the next slides indicates the percentage of radio units produced by these plants, as well as, the percentage of the defective ones among them. If a car is selected randomly and that the radio is found to be faulty, what’s the probability that the radio was manufactured in plant A? Show the tree diagram of the problem!

5. Detective radio unit Produced radio unit Plant 1 %50 %A 2 %30 %B 2 % 20 %C

6. Exercises (5) The percentage of people in Qatar who are highly digitally literate who test as such by a special e-test is 80% and the percentage of those not highly digitally literate who, all the same, test as such, because if some imperfection of the testis is 2%. Assume that a person is selected at random and given the test. If the result says the person is highly digitally literate, what’s the probability that the person is as such, knowing that 10% of the population of Qatar is highly digitally literate. Show the tree diagram of the problem!

7. Exercises (6) Two identical bags has little colored balls inside them. One of the bag has two red balls and the other has one red and one yellow ball. One of the bags is selected at random and a ball from that bag is selected at random. The ball turned out to be red. What’s the probability that the other ball left in that bag is also red? Show the tree diagram of the problem!