Question

put the events in order of increasing probability.
p = 0
you roll a 6 - sided die and it lands on a multiple of 4.
you roll a 6 - sided die and it lands on 3, 4, 5, or 6.
you pull a yellow ball from a box of all yellow balls.
you pull a gray ball from a box of all pink balls.
you flip a dime and it lands on tails.

Explanation:

Step1: Calculate probability for each event

• Event 1: Roll a 6 - sided die, multiple of 4. Outcomes on die: 1,2,3,4,5,6. Multiples of 4: 4. So \( P_1=\frac{1}{6}\approx0.167 \).
• Event 2: Roll a 6 - sided die, lands on 3,4,5,6. Number of favorable outcomes: 4. So \( P_2 = \frac{4}{6}=\frac{2}{3}\approx0.667 \).
• Event 3: Pull a yellow ball from a box of all yellow balls. All balls are yellow, so \( P_3 = 1 \).
• Event 4: Pull a gray ball from a box of all pink balls. No gray balls, so \( P_4=0 \).
• Event 5: Flip a dime and it lands on tails. A dime has 2 sides (heads, tails), so \( P_5=\frac{1}{2} = 0.5 \).

Step2: Order by increasing probability

We have \( P_4 = 0 \), \( P_1=\frac{1}{6}\approx0.167 \), \( P_5 = 0.5 \), \( P_2=\frac{2}{3}\approx0.667 \), \( P_3 = 1 \). So the order is: You pull a gray ball from a box of all pink balls (\( P = 0 \)), You roll a 6 - sided die and it lands on a multiple of 4 (\( P=\frac{1}{6} \)), You flip a dime and it lands on tails (\( P = \frac{1}{2} \)), You roll a 6 - sided die and it lands on 3,4,5, or 6 (\( P=\frac{2}{3} \)), You pull a yellow ball from a box of all yellow balls (\( P = 1 \)).

Answer:

1. You pull a gray ball from a box of all pink balls
2. You roll a 6 - sided die and it lands on a multiple of 4
3. You flip a dime and it lands on tails
4. You roll a 6 - sided die and it lands on 3, 4, 5, or 6
5. You pull a yellow ball from a box of all yellow balls