Answer the following questions. Draw the tree diagram for all the nine questions. Show the complete and legible answers/solutions.

Question 1:

A safety engineer claims that only 40% of all workers wear safety helmets when they eat lunch at the workplace. Assuming that his claim is right, find the probability that 4 of 6 workers randomly chosen will be wearing their helmets while having lunch at the we place. "5: twouwi 49x A card is drawn from a deck of cards, the result recorded, and the card replaced If the experiment is repeated 5 times, what is the probability of obtaining 2spades and 1 heart? 2 spade multinomial 1 heart 7 other combiThe probabilities are .40, .20, .30 and .10 respectively, that a delegate to a certain seminar arrived by air, bus, automobile or train. What is the probability that among 9 delegates randomly selected at this seminar, 3 arrived by air, 3 by bus,1 by automobile and 2 arrived by train. box contains 5 red and 10 white marbles. If 8 marbles are to be chosen at random without replacement. Determine the probability that a)- 4 will be red b). All will be white In an NBA championship series, the team which wins four games out of seven will be the winner. Suppose that team A has probability 0.55 of winning over the team B and both teams A and B face each other in the championship games. a. What is the probability that team A will win the series in six games? b. What is the probability that team A will win the series? c. If both teams face each other in a regional playoff series and the winner is decided by winning three out of ve games, what is the probability that team A will win the playoff? The ABC company manufactures toy robots. About 1 toy robot per 100 does not work. You purchase 35 ABC toy robots. What is the probability that exactly 4 do not work Births in a hospital occur randomly at an average rate of 1.8 births per hour. a. What is the probability of observing 4 births in a given hour at the hospital? b. What about the probability of observing more than or equal to 2 births in a given hour at the hospital? A company makes electric motors. The probability an electric motor is defective is 0.01. What is the probability that a sample of 300 electric motors will contain exactly 5 defective motors? In certain industry facility accidents occur infrequently. It is known that the probability of an accident on any given day is .005 and accidents are independent of each other. a. What is the probability that any given period of 400 days there will be no accident on one day? b. What is the probability that there are at most three days with an accident