If a person told you what month he was born, would it be unusual to guess the date of his birth ( not including the year)? Justify your answer. (Note: An event is to be considered "unusual" if its probability is less than or equal to 0.05.)
It would be unusual.
1/30 = 0.0333
1/28=0.0357
1/31=0.0323
ITS UNUSUAL SINCE BOTH PROBABILITIES ARE LESS THEN 0.05%.
To determine if it would be unusual to guess the date of someone's birth (excluding the year) based on knowing only the month, we need to consider the probability of making an accurate guess.
There are 12 months in a year, so the probability of randomly guessing the correct month is 1/12 or approximately 0.0833.
However, guessing the specific date within a month is much more challenging. For example, if we consider a non-leap year with 365 days, the probability of guessing the correct date is 1/365, which is approximately 0.0027.
To calculate the overall probability of correctly guessing both the month and the date, we need to multiply the two probabilities together.
0.0833 (probability of guessing the month) * 0.0027 (probability of guessing the date) = 0.000225 or approximately 0.0225%.
This means that the probability of correctly guessing a person's birth date (excluding the year) based only on knowing the month is extremely low, at around 0.0225%. Since this probability is significantly less than 0.05, it would be considered unusual to accurately guess someone's birth date with only the month as a clue.
To determine whether it would be unusual to guess the date of someone's birth given the month, we need to calculate the probability of guessing the correct date.
First, we need to consider how many days each month has. Since not all months have the same number of days, the probability of guessing the correct date will depend on the specific month. Here are the number of days in each month:
- January: 31 days
- February: 28 or 29 days (depending on whether it's a leap year)
- March: 31 days
- April: 30 days
- May: 31 days
- June: 30 days
- July: 31 days
- August: 31 days
- September: 30 days
- October: 31 days
- November: 30 days
- December: 31 days
Let's assume it's not a leap year, so February has 28 days.
Next, we need to calculate the total number of possible dates in a year, excluding the year itself. Since each month has a different number of days, we need to sum the number of days for each month:
31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31 = 365
So, there are 365 possible dates in a year.
Now, since the person has only told us the month of their birth, we have to consider the probability of guessing the correct date within that specific month. Since some months have fewer days (e.g., February with 28 days), and some have more (e.g., January, March, May, July, August, October, and December with 31 days), the number of possible dates within a specific month will vary.
The probability of guessing the correct date is calculated by taking the reciprocal of the number of possible dates within that month. For example, if a person was born in February, the probability of guessing the correct date would be 1/28.
To determine if guessing the date of birth given the month is unusual, we need to compare the probability to the threshold of 0.05 (5%). If the probability is less than or equal to 0.05, it would be considered unusual.
Let's calculate the probabilities for each month:
- January: 1/31
- February: 1/28
- March: 1/31
- April: 1/30
- May: 1/31
- June: 1/30
- July: 1/31
- August: 1/31
- September: 1/30
- October: 1/31
- November: 1/30
- December: 1/31
Comparing each probability to 0.05, we can determine whether it would be considered unusual to guess the date of birth based on the month.