You roll a die (with numbers 1-6 on each of 6 sides) and then spin a spinner tha

Question

You roll a die (with numbers 1-6 on each of 6 sides) and then spin a spinner that has equal chance of landing on a red, yellow, or green space. 9. a. Draw a tree diagram, create a table, or make a list that shows how many outcomes are possible b. Calculate the outcomes using multiplication. c. What is the probability of rolling a 6 and then having the spinner land on yellow? i. Use your work in (a) to determine the probability ii. Use fraction multiplication/addition to determine the probability. d. What is the probability of rolling an even number and then having the spinner land on yelow? i. Use your work in (a) to determine the probability i. Use fraction multiplication/addition to determine the probability

Explanation / Answer

(a)

When we roll a die possible outcomes are 1, 2, 3, 4, 5, and 6. And it is given that spinner has three equal sections: red (R), yellow (Y) and green (G). Since die and spinner are independent from each other so possible outcomes are:

6 * 3 = 18

Following is the list of the outcomes:

b)

When we roll a die possible outcomes are 1, 2, 3, 4, 5, and 6. And it is given that spinner has three equal sections: red (R), yellow (Y) and green (G). Since die and spinner are independent from each other so possible outcomes are:

6 * 3 = 18

(c)(i)

Out of 18 possible outcomes, 1 outcome showing a 6 and Yellow so

P(6Y) =1 /18

(ii)

The probability of getting a 6 is

P(6 ) = 1/6

The probability of getting a Yellow on spinner is

P(Y) = 1/3

So by the multiplication rule, the required probability is

P(6 and yellow) = P(6)P(Yellow) = (1/6) * (1/3) = 1/18

(d)

(i) Out of 18 possible outcomes, 3 outcomes (2Y, 4Y, 6Y) showing an even number and Yellow so

P(even and Yellow) = 3/ 18 =1/6

(ii)

The probability of getting an even number is

P(an even ) = 3/6 = 1/2

The probability of getting a Yellow on spinner is

P(Y) = 1/3

So by the multiplication rule, the required probability is

P(even and yellow) = P(an even)P(Yellow) = (1/2) * (1/3) = 1/6

Outcomes 1 R 1 Y 1 G 2 R 2 Y 2 G 3 R 3 Y 3 G 4 R 4 Y 4 G 5 R 5 Y 5 G 6 R 6 Y 6 G

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