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15 Oct 2023, 03:32
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Tablet Computer: 5/36
Both prizes: 1/18
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
69% (02:20) correct
31%
(02:47)
wrong
based on 2144
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At an end-of-year party for the employees of a certain company, Martha has been given an opportunity to win as many as two prizes. She must draw, at random, exactly one numbered card from each of two boxes—each of which, in turn, contains exactly six cards, numbered from 1 to 6. If the sum of the two numbers is equal to 8, then Martha will win a tablet computer. And, if at least one of the two numbers is a 2, then Martha will win a smartphone.
Select the probability that Martha will win a Tablet computer, and select the probability that Martha will win Both prizes. Make only two selections, one in each column.
Select the probability that Martha will win a Tablet computer, and select the probability that Martha will win Both prizes. Make only two selections, one in each column.
| Tablet Computer | Both prizes | |
| 1/6 | ||
| 3/8 | ||
| 2/9 | ||
| 1/18 | ||
| 5/18 | ||
| 5/36 |
ShowHide Answer
Official Answer
Tablet Computer: 5/36
Both prizes: 1/18
15 Oct 2023, 09:42
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At an end-of-year party for the employees of a certain company, Martha has been given an opportunity to win as many as two prizes. She must draw, at random, exactly one numbered card from each of two boxes—each of which, in turn, contains exactly six cards, numbered from 1 to 6. If the sum of the two numbers is equal to 8, then Martha will win a tablet computer. And, if at least one of the two numbers is a 2, then Martha will win a smartphone.
Select the probability that Martha will win a Tablet computer, and select the probability that Martha will win Both prizes. Make only two selections, one in each column.
Since the answer for first column is the probability that Martha will win just the tablet and the answer for the second column is the probability that she will win both prizes, we will use constraints that we discover in finding the answer for the first column in finding the answer for the second column. So, let's find the answer for the first column first.
For Martha to win a tablet computer, the sum of the numbers on the two cards must be 8.
The total number of ways she can draw the two cards is 6 x 6 = 36.
The ways she can draw cards whose numbers sum to 8 are the following:
2 and 6
3 and 5
4 and 4
5 and 3
6 and 2
Since there are 5 such pairs, the probability that Martha will win a tablet computer is 5/36.
Then, of the 5 ways she can win a tablet computer, 2 include a 2. So, she has 2 ways to win both a tablet computer and a smartphone. Thus, the probability that she'll win both prizes is 2/36 or 1/18.
Correct Answer
Select the probability that Martha will win a Tablet computer, and select the probability that Martha will win Both prizes. Make only two selections, one in each column.
Since the answer for first column is the probability that Martha will win just the tablet and the answer for the second column is the probability that she will win both prizes, we will use constraints that we discover in finding the answer for the first column in finding the answer for the second column. So, let's find the answer for the first column first.
For Martha to win a tablet computer, the sum of the numbers on the two cards must be 8.
The total number of ways she can draw the two cards is 6 x 6 = 36.
The ways she can draw cards whose numbers sum to 8 are the following:
2 and 6
3 and 5
4 and 4
5 and 3
6 and 2
Since there are 5 such pairs, the probability that Martha will win a tablet computer is 5/36.
Then, of the 5 ways she can win a tablet computer, 2 include a 2. So, she has 2 ways to win both a tablet computer and a smartphone. Thus, the probability that she'll win both prizes is 2/36 or 1/18.
Correct Answer
5/36, 1/18
23 May 2024, 05:58
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Here is a detailed video solution for this interesting question.
See how this question can be solved in the test environment using "Owning the Dataset" approach.
Let us know if you have any questions.
See how this question can be solved in the test environment using "Owning the Dataset" approach.
Let us know if you have any questions.
