Question

Three cards, one labeled "A," one labeled "T," and one labeled "C," are picked in random order. Based on the tree diagram, which is a valid conclusion. Select all that apply. There are three correct answers.

The probability of the letters spelling CAT is 1/6.

The probability that A will be the first letter chosen is 1/15

15 cards must be drawn to determine the probability of spelling CAT

The sample space consists of 6 outcomes.

The probability that T will be the first letter chosen is 1/3.

Answer 1

The valid conclusions based on the given tree diagram are: the probability of spelling CAT is 1/6, the probability that A will be the first letter chosen is 1/15, and the sample space consists of 6 outcomes.

Step-by-step explanation:

In the given question, three cards labeled 'A', 'T', and 'C' are picked in random order. To determine the valid conclusions based on the tree diagram, we need to consider the probability of certain events.

1. The probability of the letters spelling CAT is 1/6. This is because there is only one arrangement where the letters can spell CAT: C first, A second, and T last.
2. The probability that A will be the first letter chosen is 1/15. Since there are 3 cards in total, and A is only on one of those cards, the probability of choosing A first is 1/3. Then, the probability of choosing A as the first letter is 1/3 multiplied by 1/5 (since there are 5 remaining cards after choosing A first), which equals 1/15.
3. The sample space consists of 6 outcomes. This is because there are 3 cards, and for each card chosen as the first letter, there are 2 remaining cards to choose from for the second letter, and then only 1 card remaining for the third letter. So the total number of outcomes is 3 x 2 x 1 = 6.
4. The probability that T will be the first letter chosen is 1/3. Similar to the probability of choosing A first, the probability of choosing T as the first letter is 1/3, since there is only 1 T card out of the 3 cards in total.

Therefore, the valid conclusions are:

• The probability of the letters spelling CAT is 1/6.
• The probability that A will be the first letter chosen is 1/15.
• The sample space consists of 6 outcomes.

Answer 2

The probability of the letters spelling CAT is 1/6; the sample space consists of 6 outcomes; the probability that T will be the first letter chooses in 1/3

If you count the amount of options at the end there are 6 which means the sample space is 6 and that you have a 1/6 chance of getting any of the options. Because there are only 3 cards, there is a 1/3 chance of any given card being chosen first.