Help, i keep on getting probability >1

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In summary, the probability of rolling at least one 4 when rolling a fair die twice is 11/36. This can be calculated by counting the possible outcomes or by recognizing it as the complement of the probability of getting exactly zero 4s.
  • #1
Roll a fair die twice and find the probability of at least one 4
here's what i did:

P(A) = |A|/|Ω| = (6C1*6C0+6C1*6C1)/(6C1*6C1)
And i get the answer as 42/36 and the real answer is 5/36
what did I do wrong
 
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  • #2
huan.conchito said:
Roll a fair die twice and find the probability of at least one 4
here's what i did:

P(A) = |A|/|Ω| = (6C1*6C0+6C1*6C1)/(6C1*6C1)
And i get the answer as 42/36 and the real answer is 5/36
what did I do wrong
Although enumeration isn't the most efficient solution to probability problems, sometimes it can show where errors are occurring. All possible 36 outcomes of 2 rolls of a fair die are shown below. Those containing At Least One (1) "Four (4)" are highlited. By counting the highlited cases below, it can be seen that exactly (11) cases out of (36) show at least one (1) "Four (4)". Therefore, the required probability is (11/36).

Roll
AB
==
11
12
13
14
15
16

21
22
23
24
25
26

31
32
33
34
35
36

41
42
43
44
45
46


51
52
53
54
55
56

61
62
63
64
65
66
==

~~
 
  • #3
huan,

xanthym is right; it's hard to argue with a 100% coverage test!

Another way to get the same answer (and it works on LOTS of probability problems) relies on the fact that "getting at least one 4" and "getting exactly zero 4s" are mutually exclusive and collectively exhaustive. In other words, all possible outcomes are included in one or the other but not both of these. So their probabilities have to sum to 1. But the probability of "getting exactly zero 4s" is easy to calculate; it's just 5/6 *5/6 = 25/36. So the prob of "getting at least one 4" is 1- 25/36 = 11/36
 

1. What does it mean when probability is greater than 1?

When a probability is greater than 1, it means that the event has a higher chance of occurring than not occurring. This is not a valid probability value as it violates the fundamental rule of probability which states that all probabilities must be between 0 and 1.

2. How does probability greater than 1 affect my data analysis?

If your data contains probabilities greater than 1, it can significantly affect your analysis and lead to erroneous conclusions. It is important to check your data for any values that are greater than 1 and correct them before proceeding with your analysis.

3. What could be causing my probability values to be greater than 1?

There are a few possible reasons for this. One common reason is that the sample size is too small, leading to unreliable probability estimates. Another reason could be errors in data collection or calculation. It is important to thoroughly check your data and calculations to identify the cause.

4. How can I fix probability values that are greater than 1?

If you have identified that your data contains probability values greater than 1, you can fix this by rescaling the probabilities. This involves dividing each probability by the sum of all probabilities in the dataset. This will ensure that all probabilities are between 0 and 1 and maintain the relative probabilities between events.

5. Can probability ever be greater than 1?

No, probability cannot be greater than 1. As mentioned earlier, this violates the fundamental rule of probability and is not a valid probability value. If you encounter a probability value greater than 1, it is important to investigate and correct the issue.

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