1. A fair is rolled. What is the probability of getting: a) a multiple of 3? b) a number greater than 6? c) a prime number? d) a number less than 7? 2. A circle is divided into 12 equal parts to form a spinner. It is numbered as shown on the right. When the pointer is spun, what is the probability that it will stop at: a) 10? b) a number between 4 and 12? c) a number less than 9? d) a number greater than or equal to 2? e) a negative number? f) a square number? (NOTE: Assume that the pointer will never stop exactly in any of the lines separating the sectors.) ETTI OL 23 A 5 6
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1.
a) There are 6 multiples of 3 on a fair die (3, 6, 9, 12, 15, 18). The total numbers on the die are 6. Therefore, the probability of rolling a multiple of 3 is 6/6 or 1.
b) There are no numbers greater than 6 on a fair die. Therefore, the probability of rolling a number greater than 6 is 0.
c) There are 3 prime numbers on a fair die (2, 3, 5). The total numbers on the die are 6. Therefore, the probability of rolling a prime number is 3/6 or 1/2.
d) There are 6 numbers less than 7 on a fair die (1, 2, 3, 4, 5, 6). The total numbers on the die are 6. Therefore, the probability of rolling a number less than 7 is 6/6 or 1.
2.
a) The spinner has 12 equally likely outcomes, including the number 10. Therefore, the probability of stopping at 10 is 1/12.
b) The spinner has 12 equally likely outcomes. The numbers between 4 and 12 are 4, 5, 6, 7, 8, 9, 10, 11, and 12. There are 9 numbers between 4 and 12. Therefore, the probability of stopping at a number between 4 and 12 is 9/12 or 3/4.
c) The spinner has 12 equally likely outcomes. The numbers less than 9 are 1, 2, 3, 4, 5, 6, 7, and 8. There are 8 numbers less than 9. Therefore, the probability of stopping at a number less than 9 is 8/12 or 2/3.
d) The spinner has 12 equally likely outcomes. The numbers greater than or equal to 2 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. There are 11 numbers greater than or equal to 2. Therefore, the probability of stopping at a number greater than or equal to 2 is 11/12.
e) The spinner does not contain any negative numbers. Therefore, the probability of stopping at a negative number is 0.
f) The spinner does not contain any square numbers. Therefore, the probability of stopping at a square number is 0.