Statistics and Probability Answers

Let T be a random variable giving the number of spots that appear on top when a die is rolled. List the elements of the sample space S for the number of spots that appear on top when a die is rolled and assign a value to each sample point. 

Consider a sample space S={E1, E2, E3, E4,} where P(E1) = P(E4) = 0.3 and P(E2) = P(E3) = 0.2

Define the events :

A={E1, E2}

B={E2, E3}

C={E3, E4}

Which of the following pairs of events are independent? Explain.

1. A and B

2. B and C

3. A and C

Only 27% of U.S adults get enough leisure time to exercise to achieve cardiovascular fitness. Choose 3 adults at random. Find the probability that A: All 3 get enough daily exercise B: At least 1 of the 3 gets enough exercise.

At the begining of each day, the three motors required for the operation of a machine are checked and tested. These motors then have probabilities of 7/8, 5/6 and 2/3 of continuously operating through out a working day. If the production can be maintained as long as two of three motors are operating, calculate the probability of the machine not failing on a particular day. Calculate also the probability of the machine failing for a particular day.

A, B and C are bidding for a contract. It is believed that A has exactly half the chance that B has, B in turn 4/5th as likely as C to win the contract. What is the probability for each to win the contract?

4 out of 12 television set chosen at of random are defentive, if three of the tv set are choosen at of random for shipment to a hotel, how many defective set can they expect

If B = the probability I will make a basket in today's' basketball game and S = the probability that I will sprain my wrist today then write out as a complete sentence what the probability equation P ( B | S ) = 0.005 means.

Suppose that a die is rolled twice. What are the possible values and their corresponding probabilities that the following random variables can take on: (a) the maximum value to appear in both rolls; (b) the sum of the values obtained from the two rolls; (c) the value of the first roll minus the value of the second roll?

A pack of playing cards is being used by four players for a game of bridge, so each is dealt 13 cards. The King, Queen and Jack are referred to as picture cards. Find the probability that a bridge hand (13 cards) contains (a) 3 spades, 4 diamonds, 1 heart and 5 clubs; (b) 3 aces and 4 picture cards. 

Show that if events A and B are independent, then the following pairs of events are also independent. (a) A and B¯ (b) A¯ and B¯.