Working with Events Topic Index | Algebra Index | Regents Exam Prep Center

Answer the following questions dealing with mutually exclusive events, independent events, and complements of events.

 1. A pair of dice is rolled.  Two possible events are rolling a number greater than 8 and rolling an even number.  Are these two events mutually exclusive events? Choose: yes no Answer Look at the Sample Space for Dice. Numbers greater than 8: 9, 10, 11, 12 Even numbers: 2,4,6,8,10,12 The two events SHARE outcomes. They are not mutually exclusive.

 2. A pair of dice is rolled.  Two possible events are rolling a number less than 5 and rolling a number which is a multiple of 5.  Are these two events mutually exclusive? Choose: yes no Answer Look at the Sample Space for Dice. A number less than 5:  2,3,4 A multiple of 5: 5,10 These events do NOT share any outcomes. They ARE mutually exclusive.

 3. A pair of dice is rolled.  A possible event is rolling a multiple of 5.  What is the probability of the complement of this event? Choose:  2/36 12/36 29/36 32/36 See Sample Space for Dice Answer Multiple of 5: 5,10 Look at the Sample Space for Dice to see the number of possible 5's or 10's that could be rolled.  There are 7. P(multiple of 5) = 7/36. P(complement)=1-7/36=29/36

 4. A pair of dice is rolled.  Two possible events are rolling a number which is a multiple of 3 and rolling a number which is a multiple of 5.  Are these two events mutually exclusive? Choose: yes no See Sample Space for Dice Answer Look at the Sample Space for Dice. Multiple of 5: 5, 10 Multiple of 3: 3, 6, 9, 12 These events do NOT share any outcomes. They ARE mutually exclusive.

 5. A pair of dice is rolled and the resulting number is odd.  Which of the following events is the complement of this event? 1.  A number greater than 8 is rolled. 2.  An even number is rolled. 3.  A number less than 5 is rolled. 4.  A multiple of 5 is rolled. Choose: 1 2 3 4 See Sample Space for Dice Answer Look at the Sample Space for Dice. All numbers that are NOT odd numbers are even numbers.  The correct choice is 2.

 6. A paper bag contains 15 slips of paper.  Eight of them are blue and are numbered from 1 to 8.  Seven of them are pink and are numbered from 1 to 7.  What is the probability of drawing a slip of paper with an even number? Choose: 8/15 7/15 6/15 5/15 Answer Blue even: 2,4,6 8 = 4 slips Pink even: 2,4,6 = 3 slips 7 slips out of 15 are even. P(even) = 7/15

 7. A paper bag contains 15 slips of paper.  Eight of them are blue and are numbered from 1 to 8.  Seven of them are pink and are numbered from 1 to 7.  A slip is drawn from the bag and then replaced.  A second slip is drawn.  Are these two events independent? Choose: yes no Answer By replacing the slip, the sample space for both events remains at 15.  The second event is not affected by the first event. They are independent events.

 8. A paper bag contains 15 slips of paper.  Eight of them are blue and are numbered from 1 to 8.  Seven of them are pink and are numbered from 1 to 7.  A possible event is that a blue slip is chosen.  What is the probability of the complement of this event? Choose: 8/15 7/15 1/3 1/2 Answer P(blue) = 8/15. P(Complement) = 1 - 8/15 = 7/15

 9. A paper bag contains 15 slips of paper.  Eight of them are blue and are numbered from 1 to 8.  Seven of them are pink and are numbered from 1 to 7.  You wish to draw a blue slip on the first draw and a pink slip on the second draw.  The first slip is NOT replaced after being drawn.  Are these events independent? Choose: yes no Answer By not replacing the slip, the sample space for the second event is being affected. The second event is now dependent upon the outcome of the first event.

10. Juan spins the spinner shown below.  He notes the area on which the arrow stops, and then spins it a second time.  Find the probability that the outcome of the two spins is:
 a.)  red both times b.)  white first, blue second c.)  white first, red second d.)  not blue both times

11. A sack contains marbles of three different colors:  8 black, 6 white, and 4 red.  Three marbles are selected at random, without replacement.  Find the probability that the selection contains each of the outcomes listed below.  Express the answer as a decimal to the nearest hundredth.
 a.)  three black marbles b.)  three white marbles c.)  one white marble followed by two       black marbles d.)  a red, a black and a white marble,       in that order e.)  a red marble and two white marbles,       in any order

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