Probability (Day 2) – Green Problems

Find each event’s probability by showing all of the possible outcomes.
1. / You toss three coins and get three heads. /
2. / You toss three coins. You get one head and two tails (order doesn’t matter)
3. / You toss a coin and roll a die. You toss tails and roll an even number.
You roll a die twice. Record all of the possible outcomes. What is the probability that you roll each of the following pairs on numbers?
4. / 6 and then 5 /
5. / 6 and then 2 or 5
6. / 6 and then a number less than 4
7. / 1 and then 1
8. / An even number and then 2 or 5
9. / An even number and then an odd number
10. / Use the letters E, P, S and T.
a. / How many possible arrangements of the letters are there?
b. / How many arrangements form real English words?
c. / What is the probability that an arrangement of these letters chosen at random will form an English word?
11. / Anderson will roll two standard six-sided dice once. What is the probability that the two numbers rolled will be the same? Express your answer as a common fraction.
12. / A game board is constructed by shading two of the regions formed by the altitudes of an equilateral triangle as shown. What is the probability that the tip of the spinner will come to rest in a shaded region? Express your answer as a common fraction. /
13. / Two fair coins are flipped. What is the probability that both show heads? Express your answer as a common fraction.
14. / This game is made with 36 unit squares. A game show company put prizes behind the shaded squares on the board, but the contestants can’t see the shading. What is the probability that a contestant choosing a unit square from the board at random selects a square with a prize behind it? Express your answer as a common fraction. /
15. / What is the probability of getting an even number when a fair six-sided die is rolled? Express your answer as a common fraction.
16. / In a coin tossing game, seven tosses result in seven heads. What is the probability that the next toss will also be a head? Explain your answer.
17. / If you pick a letter at random from the alphabet, what is the probability that it is in the word mathematics? Express your answer as a common fraction.
18. / A bag contains 3 red and 5 blue marbles. If one marble is randomly drawn from the bag, what is the probability that it is blue? Express your answer as a common fraction.
19. / Chen’s math teacher gives homework four out of every five school days. Her science teacher gives homework three out of every four school days. What is the probability that on a particular school day Chen does not have homework in either subject? Express your answer as a common fraction.

Probability (Day 2) – Green Solutions

1. / / 2. / / 3. /
4. / / 5. / / 6. /
7. / / 8. / / 9. /
10. / a. / 24
b. / Three: pest; pets and step
c. /
11. / If we make a table of all of the possible rolls of two dice, we see that there are 36 possibilities. Only six of these will have the same rolled number. Thus, the probability of rolling the same number on each die is 6/36 – 1/6.
12. /
13. / Using logical reasoning, the probability of getting heads when a coin is flipped is . Thus, the probability of getting two heads when flipping two coins is x = . Another solution is to elaborate the sample space, which is HH, HT, TH and TT. There are four possible outcomes, and one of these outcomes is HH, two heads. In either case, the probability is .
14. / Ten of the 36 unit squares are shaded, so the probability that a contestant will select a unit square with a prize behind it is 10/36 or 5/18.
15. / A tair 6-sided die has 3 even numbers and 3 odd numbers. The probability of rolling an even number is 3/6 or ½.
16. / The probability that the next toss will be a head is ½. The first seven results do not affect the next toss. There is one favorable outcome our of two possible outcomes.
17. /
18. / Because there are 3 red and 5 blue marbles, there are 8 ways to choose 1 marble and 5 ways to choose a blue marble. There is, therefore, a probability that a randomly chosen marble will be blue.
19. /