Question

put the events in order of increasing probability.
p = 0
on a spinner with just 1 and 2, you spin a 9.
you flip a dime and it lands on heads.
on a spinner with just 5 and 7, you spin an odd number.
you roll a 6 - sided die and it lands on 1 or 6.
you roll a 6 - sided die and it lands on 2, 3, 4, 5, or 6.
p = 1

Explanation:

Step1: Calculate probability for each event

• Event 1: Spinner with 1 and 2, spin 9. Possible outcomes: 1,2. Favorable: 0. Probability $P_1 = \frac{0}{2} = 0$.
• Event 2: Flip dime, land heads. Possible outcomes: heads, tails. Favorable: 1. Probability $P_2 = \frac{1}{2} = 0.5$.
• Event 3: Spinner with 5 and 7, spin odd. Both 5,7 are odd. Favorable: 2. Probability $P_3 = \frac{2}{2} = 1$.
• Event 4: Roll 6 - sided die, land 1 or 6. Possible outcomes: 1,2,3,4,5,6. Favorable: 2. Probability $P_4 = \frac{2}{6}=\frac{1}{3}\approx0.333$.
• Event 5: Roll 6 - sided die, land 2,3,4,5,6. Possible outcomes: 1,2,3,4,5,6. Favorable: 5. Probability $P_5 = \frac{5}{6}\approx0.833$.

Step2: Order by increasing probability

Sort the probabilities: $0$ (Event 1) < $\frac{1}{3}$ (Event 4) < $0.5$ (Event 2) < $\frac{5}{6}$ (Event 5) < $1$ (Event 3).

Answer:

1. On a spinner with just 1 and 2, you spin a 9.
2. You roll a 6 - sided die and it lands on 1 or 6.
3. You flip a dime and it lands on heads.
4. You roll a 6 - sided die and it lands on 2, 3, 4, 5, or 6.
5. On a spinner with just 5 and 7, you spin an odd number.