Exclude leap years from the following calculations and...

Exclude leap years from the following calculations and assume each birthday is equally likely: (a) Determine the probability that a randomly selected person has a birthday on the 1 st day of a month. Interpret this probability. (b) Determine the probability that a randomly selected person has a birthday on the 31 st day of a month. Interpret this probability. (c) Determine the probability that a randomly selected person was born in December. Interpret this probability. (d) Determine the probability that a randomly selected person has a birthday on November $8 .$ Interpret this probability. (e) If you just met somebody and she asked you to guess her birthday, are you likely to be correct? (f) Do you think it is appropriate to use the methods of classical probability to compute the probability that a person is born in December?

Exclude leap years from the following calculations and assume each birthday is equally likely:
(a) Determine the probability that a randomly selected person has a birthday on the 1 st day of a month. Interpret this probability.
(b) Determine the probability that a randomly selected person has a birthday on the 31 st day of a month. Interpret this probability.
(c) Determine the probability that a randomly selected person was born in December. Interpret this probability.
(d) Determine the probability that a randomly selected person has a birthday on November $8 .$ Interpret this probability.
(e) If you just met somebody and she asked you to guess her birthday, are you likely to be correct?
(f) Do you think it is appropriate to use the methods of classical probability to compute the probability that a person is born in December?

Key Concepts

Uniform Distribution

A uniform distribution is a probability distribution where every outcome in the sample space is equally likely. In the context of birthdays under the exclusion of leap years, this means that each day is assumed to be equally likely for a birthday, simplifying the calculation of the probability of any given event.

Sample Space

The sample space is the complete set of all possible outcomes in a probability experiment. For the birthday problem, it includes all possible dates in the calendar (excluding leap days), and clearly identifying this space is key to accurately calculating probabilities using the classical approach.

Classical Probability

Classical probability defines the likelihood of an event as the ratio of the number of favorable outcomes to the total number of equally likely outcomes in the sample space. This method assumes all indivisible outcomes are equally probable, which is fundamental when calculating the probability of simple events in a controlled setting.

Favorable Outcome Counting

Counting favorable outcomes involves identifying all outcomes in the sample space that satisfy the event of interest. This concept is essential in classical probability, where the probability of an event is determined by dividing the number of favorable outcomes by the total number of outcomes.

Interpretation of Probability

Interpreting probability involves understanding the calculated likelihood as a measure of chance that an event will occur, often expressed as a fraction or percentage. It provides insight into how likely it is for a randomly selected instance to exhibit a specific characteristic under the defined conditions.

Transcript

00:03 Hello hi here in this question you can see we take a calendar years right we know there are leap years are there so the question is basically from one of the day we are going to select and what will be the probability of those days so first part of the question it is asking us what is the probability that a randomly selected person has a birthday on first day of a month so you know if you take four years 4 years in 4 years out of 4 years 3 years will be 3 l .m .o.

00:50 Non -lapius.

00:51 So it will contain 3 to 365 days.

00:54 And 4th day, 4th year will be a leapio.

00:58 So total there will be 1 ,461 days will be there.

01:05 Right? and every after every 4 years, the same numbers will repeat.

01:11 So knowing that, if you take first part of the question, what is the probability that? that the person selected will be having birthday on first day of a month so first day of a month means how many months are there you know one year there are 12 months are there so 12 into 4 48 month will be there right so probability of getting first day of a month as birthday will be given by i am writing probability of a 48 days will be there out of 1 ,461 this will be the required probability.

01:53 Now take second question.

01:58 What will be the probability? that randomly selected person having birthday on 31st day of month.

02:06 So how many months having 31 days? out of 12 months, seven months in a year has 31 days.

02:19 You can check january, march, may like that, just check.

02:24 You can see seven months other.

02:26 So in a year seven months.

02:27 So in a year, seven month.

02:28 So in a four year, there will be seven into four, that is 28 favorable cases will be there.

02:34 So i'm calling this event as b, in probability of getting 31 days or 30 first day as a birthday will be 28 out of 1 ,461...

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