This handy Spectrum Math Grade 7 Answer Key Chapter 7 Lesson 7.6 Understanding Compound Events provides detailed answers for the workbook questions
Spectrum Math Grade 7 Chapter 7 Lesson 7.6 Understanding Compound Events Answers Key
The Fundamental Counting Principle states that when an experiment is conducted that is considered a compound event, or an event that has more than one element, the number of possible outcomes can be calculated by considering the number of possible outcomes for each element. The number of possible outcomes for the first element (a) can be multiplied by the number of possible outcomes for the second element (b) to find the total number of possible outcomes (0). So, a × b = 0.
There are 3 balls (yellow, red, and green) in one bag and 4 balls (purple, blue, white, and black) in another bag. If a person draws one ball from each bag, how many possible outcomes are there?
Step 1: Find the number of outcomes for the first event. 3
Step 2: Find the number of outcomes for the second event. 4
Step 3: Multiply these together. 3 × 4
Step 4: State the number of possible outcomes for the combined event. 12
Use the Fundamental Counting Principle to find the number of possible outcomes for each compound event described.
Question 1.
a. rolling two dice that are numbered 1-6
Answer:
36,
Explanation:
Given rolling two dice, number of outcomes for first event is 6 and number of outcomes for second event is 6 so, number of possible outcomes for the compound event is 6 X 6=36.
b. flipping a coin and rolling a die numbered 1-6
Answer:
12,
Explanation:
As we know that number of outcomes for flipping a coin is 2 and number of outcomes for rolling a die numbered is 6 so, the possible outcomes for the compound event is 2 X 6 = 12.
Question 2.
a. spinning a 4-part spinner and flipping a coin
Answer:
8,
Explanation:
As we know that number of outcomes for spinning a 4-part spinner is 4 and number of outcomes for flipping a coin is 2 so, number of possible outcomes for the compound event is 4 X 2 =8.
b. pulling o card from a full deck and flipping a coin
Answer:
104,
Explanation:
As we know that number of outcomes for pulling o card from a full deck card is 52 and no of outcomes for for flipping a coin is 2 so, number of possible outcomes for the compound event is 52 X 2=104.
Question 3.
a. spinning a 6-part spinner and rolling a die numbered 1-6
Answer:
36,
Explanation:
As we know that umber of outcomes for spinning 6-part spinner is 6 and number of outcomes for rolling a a die is 6 so , number of possible outcomes for the compound event is 6 X 6 = 36.
b. flipping a coin and rolling two dice numbered 1-6
Answer:
72,
Explanation:
As we know that number of outcomes for flipping a coin is 2 and number of outcomes for two dice numbered is 36 so, number of possible outcomes for the compound event is 2 X 36 = 72.
Question 4.
a. spinning a 4-part spinner and pulling a card from a full deck
Answer:
208,
Explanation:
As we know that number of outcomes for 4-part spinner is 4 and number of outcomes for pulling a card from a full deck is 52 so, number of possible outcomes for the compound event is 4 X 52 =208.
b. flipping 2 coins and roIling 2 dice numbered 1-6
Answer:
144,
Explanation:
As we know that number of outcomes for flipping 2 coins are 4 and number of outcomes for rolling 2 dice numbered is 36 so, number of possible outcomes for the compound event is 4 X 36 =144.
Use the Fundamental Counting Principle to find the number of possible outcomes. Show your work.
Question 1.
3 coins are tossed and Iwo six-sided dice are rolled. How many possible outcomes are there?
There are _____________ possible outcomes.
Answer:
288,
Explanation:
Given that number of outcomes when 3 coins are tossed are 8 and number of outcomes two six- sided dice are rolled is 36 so, the number of possible outcomes are 8 X 36 = 288.
Question 2.
Jed is shopping. He is looking at 5 different ties, 3 different sweaters, and LI different shirts. How many
possible combinations can he make?
Jed can make _____________ possible combinations.
Answer:
765 ,
Explanation:
Given Jed is shopping , looking for number of different ties are 5 ,number of different sweaters are 3 and number of different shirts are LI that is 51 so number of possible combinations Jed can make is 5 X 3 51 = 765.
Question 3.
Miranda’s jewelry box contains 8 necklaces, 10 pairs of earrings, and LI bracelets. How many combinations, which contain all 3 kinds of jewelry, can she make?
Miranda can make ____________ combinations of jewelry.
Answer:
4,080 ,
Explanation:
Given jewelry box contains number of necklaces are 8, number of pairs of earrings are 10 and number of bracelets are 51 so, number of combinations of all 3 kinds can Miranda make is 8 X 10 X 51 = 4,080.
Question 4.
Robert has to color in LI different shapes (circle, square, triangle, and rectangle) and has 5 colors to choose from (green, yellow, red, blue, and orange). If he can only use each color one time, how many ways can he color the shapes?
Robert can color the shapes _____________ different ways.
Answer:
255,
Explanation:
Given number of different shapes do Robert has is 51 and number of to choose is 5 so, number of different shapes can Robert can color is 51 X 5 = 255.
Question 5.
Spencer needs to put on gloves, a hat, and a scarf. He has 5 hats, 4 pairs of gloves, and 9 scarves to choose from. How many combinations of gloves, hat, and scarf can Spencer make?
Spencer can make _____________ combinations.
Answer:
180,
Explanation:
Given no of hats are 5 , no of pairs of gloves are 4 and no of scarves are 9 so, number of combinations that spencer can make are
5 X 4 X 9 =180 .
Question 6.
Pilar wants to cook a meal that consists of a meat, a starch, and a vegetable. At the grocery store there are 8 chokes of meat, 8 choices of vegetables, and 3 choices of starches. How many possible combinations can Pilar make?
Pilar can make _____________ combinations.
Answer:
192,
Explanation:
Given at grocery number of chokes of meat are 8 ,number of choices of vegetables are 8 and number of choices of starches are 3 so, number of possible combinations can Pilar make are 8 X 8 X 3 = 192.
Question 7.
Jacob must collect a flower, a vegetable, and an herb. In the garden, there are 10 kinds of flowers, 7 kinds of vegetables, and 4 kinds of herbs. How many combinations can Jacob make?
Jacob can make _______________ combinations.
Answer:
280,
Explanation:
Given In a garden number of kinds of flowers are 10 ,number of kinds of vegetables are 7 and number of kinds of herbs are 4 so, number of combinations can Jacob make are 10 X 7 X 4 = 280.