Question

Mrs. Parker puts students into groups for a field trip. Each group is labeled with a letter, A or B, and a number from 1 to 6. She rolls a number cube and draws a letter tile from a bag to randomly place each student in a group. What is the probability that Josie will be placed in an A group with an even number? Show your work.

Answer 1

Answer: 1/6

Explanation:

There are six possible outcomes when rolling a number cube, and two possible outcomes when drawing a letter tile.

To determine the probability that Josie will be placed in an A group with an even number, we need to find the number of outcomes that satisfy this condition and divide by the total number of possible outcomes.

The possible outcomes that satisfy the condition are:

• Group A and even number: There are three even numbers on a number cube, so the probability of rolling an even number is 3/6 = 1/2. Once an even number is rolled, there are two group A tiles left in the bag, so the probability of drawing an A tile is 2/2 = 1. Therefore, the probability of being placed in an A group with an even number is (1/2) x 1 = 1/2.

The total number of possible outcomes is:

• Six possible numbers on a number cube multiplied by two possible letters in the bag: 6 x 2 = 12

Therefore, the probability that Josie will be placed in an A group with an even number is:

• Probability = Number of outcomes that satisfy condition / Total number of possible outcomes
• Probability = 1/2 / 12
• Probability = 1/6

Therefore, the probability that Josie will be placed in an A group with an even number is 1/6.

Answer 2

Okay, here are the steps to find the probability that Josie will be placed in an A group with an even number:

1) There are 2 possible letters (A or B) and 6 possible numbers (1-6) for the groups. So there are 2 * 6 = 12 possible groups total.

2) Half of the groups (6 groups) will be A groups.

3) Half of the groups (6 groups) will have an even number (2, 4, 6)

4) So there are 6 * 6 / 12 = 1/2 = 0.5 probability that a randomly selected group will be an A group with an even number.

5) Therefore, the probability that Josie will be placed in an A group with an even number is 0.5.

Work shown:

Total groups: 12

A groups: 6

Even number groups: 6

Probability A group with even number: 6 * 6 / 12 = 1/2 = 0.5

Prob Josie in A even group: 0.5

0.5

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