1. andrew will roll a number cube and flip a coin for a probability experiment. the faces of the number cube are labeled 1 through 6. the coin can land on heads or tails. if andrew rolls the number cube once and flips the coin once, write a list that contains only the outcomes in which the number cube lands on a number less than 3? 2. a study of a population of 1,500 dogs revealed that 15 out of every 125 dogs in the population have spots on their back. based on the results of this study, how many dogs in the population do not have spots on their back? 3. for his lunch, david is making a sandwich that must consist of bread, cheese, and meat. david can choose from white, french or rye bread, either american or swiss cheese, and the choice of turkey, ham or pastrami as a meat. create a tree diagram to represent the combinations of bread, cheese, and meat david could make for his sandwich. 4. joel has an mp3 player called the jumble. the jumble randomly selects a song for the user to listen to. joel's jumble has 2 classical songs, 13 rock songs, and 5 rap songs on it. what is the probability that the first song that joel hears is a rap song? 5. you're playing a game where you defend your village from an orc invasion. there are 3 characters (elf, hobbit, or human) and 5 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from. if you randomly choose your character and tool, what is the probability that you'll be a magic elf?

Part 1)

(1,H),(2,H)(1,T),(2,T)

Part 2)

1320

Part 4)

1/4

Part 5)

1/15

Step-by-step explanation:

Part 1)

Possible outcomes of cube={1,2,3,4,5,6}

Possible outcomes of coin=(H,t}

Now,  Andrew rolls the number cube once and flips the coin once

then possible outcome that contains only the outcomes in which the number cube lands on a number less than 3 are:

(1,H),(2,H)(1,T),(2,T)

Part 2)

Given:

population=1500 dogs

spots containing dogs= 15 out of every 125 dogs in the population have spots

spots containing dogs:

                                =1500/125

                                     =12    

                                     =12*15

                                     =180    

dogs in the population that do NOT have spots on their back

=1500-180=1320

Part 4)

Given:

classical songs=2

rock songs=13

rap=5

total songs= 2+13+5

                 =20

probability that the first song that Joel hears is a rap song= 5/20

                                     =1/4

Part 5)

Given:

3 Characters= elf, hobbit, or human

4 tools= magic, sword, shield, slingshot, or umbrella

Probability of first event , P(C)= 1/3

Probability of second event, P(T)=1/5

As both events are mutually exclusive so

P(magic elf)= P(C)*P(T)

                 =1/3+1/5

                 =1/15 !

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.