Enrichment. Suppose that you are given this information about rolling a number cube.

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1 ate - Working ackward with Probabilities Suppose that you are given this information about rolling a number cube. P() P() P() an you tell what numbers are marked on the faces of the cube Work backward. Since a cube has six faces, express each probability as a fraction whose denominator is. P() P() P() So, the cube must have three faces marked with the number, two faces marked, and one face marked. Each set of probabilities is associated with rolling a number cube. What numbers are marked on the faces of each cube. P(). P(). P( or ) P() P() P( or ) P() P(factor of ) P(,, or ) Each set of probabilities is associated with the spinner shown at the right. How many sections of each color are there. P(red). P(yellow or purple) P(blue) P(purple or white) P(green) P(green or blue) 0 P(black) P(yellow, purple, or white). Suppose that you are given this information about pulling a marble out of a bag. P(green) P(blue) P(red) P(yellow) P(white) P(black) If the bag contains marbles, how many marbles of each color are there Mathematics: pplications Glencoe/McGraw-Hill 0 and onnections, ourse

2 ate - Odds People who play games of chance often talk about odds. You can find the odds in favor of an event by using this formula. odds in favor = number of ways an event can occur number of ways the event cannot occur With the spinner shown at the right, for example, this is how you would find the odds in favor of the event prime number. There are four prime numbers (,,, ). Six numbers are not prime (,,,,, 0). The odds in favor of the event prime number are or to. 0 Suppose that you spin the spinner shown above. Find the odds in favor of each event.. number greater than. number less than or equal to. even number. odd number. multiple of. factor of 0 To find the odds against an event, you use this formula. odds against = number of ways an event cannot occur number of ways the event can occur Suppose that you roll a number cube with,,,,, and marked on its faces. Find the odds against each event.. number less than. number greater than or equal to. even number 0. odd number. number divisible by. factor of. HENGE The probability of an event is. What are the odds in favor of the event the odds against the event Mathematics: pplications Glencoe/McGraw-Hill and onnections, ourse

3 ate - Spinners and More Spinners When you spin a spinner, it is not necessarily true that all outcomes are equally likely. With the spinner shown at the right, for example, you can see it is most likely that the pointer will stop in region. To find probabilities on a spinner like this, you need to consider what fraction of a complete turn of the pointer is associated with each region. In the spinner at the right, region involves about of a complete turn, so P() is about. Using the same reasoning, P() is about, P() is about, and P() is about. Estimate each probability.... P(): P(): P(): P(): P(): P(): P(): P(): P(): P(): P(): P(): Sketch a spinner that satisfies the given conditions.. P(). P(). P() P() P() P() P() P() P() P() P() P(). HENGE Use the spinner at the right. Estimate each probability. P(): P(): P(): P(): Mathematics: pplications Glencoe/McGraw-Hill and onnections, ourse

4 ate - isting Outcomes in a Table Suppose that you spin the two spinners below. What is the probability that the sum of the numbers you spin is First Spinner To find this probability, you first need to count the outcomes. One way to do this is to use a table of sums like the one at the right. From the table, it is easy to see that there are outcomes. It is also easy to see that, in of these outcomes, the sum of the numbers is. So, the probability that the sum of the numbers is is, or. Second Spinner 0 Use the spinners and the table above. Find each probability.. P(sum is ). P(sum is ). P(sum is greater than ). P(sum is less than or equal to 0) Suppose you roll two number cubes. Each cube is marked with,,,,, and on its faces. Find each probability. (Hint: On a separate sheet of paper, make a chart like the one above.). P(sum is ). P(sum is ). P(sum is an even number). P(sum is a multiple of ). P(sum is a prime number) 0. P(sum is a factor of ). P(sum is greater than ). P(sum is less than ). HENGE Here is a set of probabilities associated with two spinners. P(sum is ) = P(sum is ) = P(sum is ) = P(sum is 0) = In the space at the right, sketch the two spinners. Mathematics: pplications Glencoe/McGraw-Hill and onnections, ourse

5 ate - ependent Events If the result of one event affects the result of a second event, the events are called dependent. For example, suppose you draw one card from the set of cards shown at the right, but do not replace it. Then you draw a second card. What is the probability that you will draw the T, then an First find the probability of drawing the T. There is card marked T. P(T) 0 There are 0 cards in all. Then find the probability of drawing an after drawing the T. There are cards marked. P( after T) Now multiply. There are cards left. P(T, then ) P(T) P( after T) 0 M 0 or 0 The probability of drawing the T, then an, is. 0 card is drawn from the set of cards above, and it is not replaced. Then a second card is drawn. Find each probability.. P(, then M ). P(T, then ) T. P(, then ). P(, then ). P(, then ). P(M, then M ) bag contains two red marbles and four blue marbles. Three marbles are pulled from the bag, one at a time, and they are not replaced. Find each probability.. P(blue, then red, then blue). P(red, then blue, then red). P(three blue marbles) 0. P(three red marbles). HENGE efer to the cards at the top of the page. Suppose you draw two cards at once. Whad do you think is the probability that you draw an and an Mathematics: pplications Glencoe/McGraw-Hill and onnections, ourse