A card is drawn from a pack of 52 cards. It is then replaced to the pack of cards and a card is drawn from the pack again.Event E is the event that the first card drawn is a diamond.Event F is the event that the second card drawn is a diamond.Event G is the event that the first card drawn is red.Which of the following is/ are TRUE?I. E and F are two independent events.II. F and G are two independent events.III. E and G are mutually exclusive events.

Two fair coins are tossed. Let A be the event that the first coin displays a heads, and let B be theeven that both coins display the same outcome.(a) Are events A and B mutually exclusive?(b) Are events A and B independent?2) A card is drawn from a standard deck of 52 cards. Let A be the event that an ace is drawn and let Bbe the event that a spade is drawn.(a) Are these events mutually exclusive or non-mutually exclusive? Explain your answer.(b) Calculate the probability of event A or event B occurring (drawing an ace or a space).A dice is tossed after a card is drawn. Let C be the event that an even number is shown on the dice.(c) Are events A and C independent or non-independent?(d) Calculate the probability of events A and C occurring (drawing an ace and rolling aneven number).3) Given that
 ∪  = 0.7 and
 = 0.2, find
 and
 ∩  if:(a) A and B are mutually exclusive(b) A and B are independent4) Two dice are rolled and the sum is recorded.(a) List all possible outcomes (i.e. the sample space).(b) Calculate the probability of rolling:(i) A sum of 5(ii) A sum of 4 or less(iii) A sum of at most 11(iv) A sum that is a multiple of 3 or a multiple of 4.5) 200 people attended a blood bank and their blood types are recorded as follows: 50 have type A,65 have type B, 70 have type O and 15 have type AB.(a) Calculate the relative probability of each blood type.(b) If two people are selected without replacement, what is the probability that:(i) One person is type A and the other is type B.(ii) They both have type B blood.(iii) They both have the same type blood.6) A coin is tossed three times and the results are recorded. What is the probability of getting:(a) Three heads.(b) At least two heads.(c) At most one tail.STAT6010 27) Two unfair coins are tossed with the probability of a tail equal to 0.25. Calculate the probability ofgetting:(a) No heads.(b) Exactly one head.(c) At least one head.8) An urn contains 6 black balls, 4 white balls and 5 red balls. The balls are removed 1 at a time fromthe urn and not replaced. If 3 balls are removed, what is the probability that:(a) All three are red.(b) Two are black and one is white(c) All are the same colour(d) At least 1 is white9) 70% of houses in a residential area have an alarm. It is found that 35% of the owners of thealarmed houses have a dog and 42% of the owners of the non-alarmed houses have a dog.a) Construct a tree diagram to show all possible events and probabilities.b) A house is selected at random. Calculate the probability that the house does nothave a dog.c) If a randomly selected house is one of the houses that does not have a dog, what isthe probability that the house has an alarm?10) On any given day, the probability that an employee will drive to work is 0.5, the probabilitythat he/she will cycle to work is 0.3 and the probability that he/she will walk to work is 0.2.If he/she drives, the probability that he/she will arrive on time is 0.6 If he/she cycles, theprobability that he/she will arrive on time is 0.8. If he/she walks, the probability thathe/she will arrive on time is 0.9. An employee is selected at random.a) Calculate the probability that the employee will arrive on time for work.b) If the employee has arrived on time for work yesterday. Calculate the probabilitythat he/she walked to work yesterday.c) The employee has not arrived on time for work yesterday. Calculate the probabilitythat he/she walked to work yesterday.

Consider a deck of playing cards. Assume A = aces; B = black cards; C = diamonds;D = hearts. For each of the following, state whether the events are mutually exclusiveand collectively exhaustivea. Events A, B, C and Db. Events B, C and D

A die is thrown twice. The numbers obtained in the two throwns are recorded.Event E is the event that two prime numbers are obtained.Event F is the event that the sum of the two numbers is a prime number.Event G is the event that the product of the two numbers is a prime number.Which of the following pairs of events is / are mutually exclusive event(s)?I. E and FII. E and GIII. F and G

Which of the following statements are true? Mark all that apply.If A and B are independent events, then the probability of Event B occurring is the same whether or not Event A occurs.If events A and B are independent, then P(A and B) = P(A) + P(B)If P(A) is the probability that event A will occur, then the probability event A will NOT occur is 1 - P(A).Two events are independent if they cannot occur at the same time.If events A and B are overlapping, then P(A or B) = P(A) + P(B) - P(A and B)

A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E isQuestion 18Select one:a.4 b.48 c.51d.13