Exercises (1) 1. In the usual dice experiment, let A, B and C, be the following events: A = {1,7,6} and B = {1,2,7,5} and C = {3,5} Find the following:

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Presentation transcript:

Exercises (1) 1. In the usual dice experiment, let A, B and C, be the following events: A = {1,7,6} and B = {1,2,7,5} and C = {3,5} Find the following: 1. The union and intersection of the events A and B. 2. The complement of the event A. 3. Which two of the sets A, B and C are mutually exclusive.

Exercises (2) In the experiment consisting of tossing a coin three times and considering the sequence of heads and tails outcomes. Find the following: 1. The sample space 2. The event E that exactly two tails appear. 3. The event F that at least one head appears. 4. The event G that two tails appear in a sequence. 5. The event A that three tails appear. 6. Show the tree diagram for this experiment.

Exercises (3) In the experiment consisting of tossing a pair of dice and considering the numbers of dots falling uppermost on each dice. Find the following: 1. The sample space 2. The events E 7 that the sum of the numbers of dots falling uppermost is 7 3. The events E 9 that the sum of the numbers of dots falling uppermost is 9

Exercises (4) In the experiment consisting of guessing the number of tickets that will be sold for a play. If there are 80 seats in the theater. Find the following: 1. The sample space 2. The event E that fewer than 20 tickets will be sold. 3. The event F that at least quarter of tickets will be sold.

Exercises (5) For the experiment of the usual rolling of the dice: 1. Exhibit the probability distribution table 2. Compute the probability that the dice shows an even number of dots. 3. Compute the probability that the dice shows more than 2 dots.

Exercises (6) A pair of dice is rolled. Calculate the following probabilities: 1. The probability that the dice show different numbers. 2. The probability that the sum of the numbers shown by the two dice is The probability that the sum of the numbers shown by the two dice is The probability that the number shown on one dice is exactly 4 times that shown on the other.

Exercises (7) The next slide shows the probability distribution with a final exam scores of a Math course. If we select at random a student who has done the exam, what is the probability that her score will be: 1. More than Less than or equal greater than 50 but less or equal greater than 40 but less or equal 60

ProbabilityScore 0.01 {s 1 } The score is greater than {s 2 } The score is greater than 60 but less or equal {s 3 } The score is greater than 50 but less or equal {s 4 } The score is greater than 40 but less or equal {s 5 } The score is greater than 30 but less or equal {s 6 } The score is less than 30

Exercises (8) A card is drawn from a deck of 52 playing cards. What’s the probability that it is a queen or a heart.

Exercises (9) 1. Let E & F be mutually exclusive events and that p(E) = 0.2 and p(F) = 0.3. Compute: a. p(E∩F)b. p(EUF)c. p(E C ) d. p(E C ∩F C )e. p(E C UF C ) 2. Let p(E) = 0.3, p(F) = 0.1 and p(E∩F) = Compute: a. p(EUF) b. p(E C ∩F C )