Questions: Refer to the chart below to answer these questions. There are two boxes containing only red and purple pens. A pen is randomly chosen from each box. a. Name an event where the probability would be 1. b. Name an event where the probability would be 0. c. Name an event where the probability would be 3. Chart: BoxA purple pens 10 BoxA red pens 23 BoxB purple pens 16 BoxB red pens 8

Refer to the chart below to answer these questions.
There are two boxes containing only red and purple pens. A pen is randomly chosen from each box.
a. Name an event where the probability would be 1.
b. Name an event where the probability would be 0.
c. Name an event where the probability would be 3.

Chart:
BoxA
purple pens
10
BoxA
red pens
23
BoxB
purple pens
16
BoxB
red pens
8

Transcript text: Refer to the chart below to answer these questions. There are two boxes containing only red and purple pens. A pen is randomly chosen from each box. a. Name an event where the probability would be 1. b. Name an event where the probability would be 0. c. Name an event where the probability would be 3. Chart: BoxA purple pens 10 BoxA red pens 23 BoxB purple pens 16 BoxB red pens 8

Solution

Solution Steps

To solve these probability questions, we need to understand the composition of the boxes and the nature of probability.

a. An event with probability 1 is certain to happen. For example, if all pens in a box are of the same color, drawing that color is certain.

b. An event with probability 0 is impossible. For example, drawing a color that doesn't exist in a box.

c. Probability cannot be greater than 1, so an event with probability 3 is impossible in standard probability theory.

Step 1: Understanding the Problem

We have two boxes, Box A and Box B, each containing red and purple pens. We need to determine the probability of certain events based on the composition of these boxes.

Step 2: Calculate Total Pens in Each Box

For Box A, the total number of pens is: \[ \text{Total Box A} = 10 + 23 = 33 \]

For Box B, the total number of pens is: \[ \text{Total Box B} = 16 + 8 = 24 \]

Step 3: Determine Probability of Event a

An event with probability 1 is certain. Since both boxes contain both colors, no single color is certain to be drawn. However, if we consider the event of drawing any pen from a box, this event is certain, hence: \[ P(\text{any pen from a box}) = 1 \]

Step 4: Determine Probability of Event b

An event with probability 0 is impossible. For example, drawing a green pen from either box is impossible since there are no green pens: \[ P(\text{drawing a green pen}) = 0 \]

Step 5: Determine Probability of Event c

Probability cannot exceed 1 in standard probability theory. Therefore, an event with probability 3 is not possible: \[ P(\text{any event}) \leq 1 \]