P.3.8 Suppose that there are 50 people in a room. It can be shown (under certain
ID: 3069180 • Letter: P
Question
P.3.8 Suppose that there are 50 people in a room. It can be shown (under certain assumptions) that the probability is approximately 0.97 that at least two people in the room have the same birthday (month and date, not necessarily year). Select which statement would best explain what 0.97 means to a person who has never studied probability or statistics. O In many, many rooms each containing 50 people, 97% of the rooms will have at least two people with the same birthday. O If you have 100 rooms with 50 people, then 97 of the rooms should have at least two people with the same birthday. o Each of these statements are equivalent statements about probability. O Neither of these statements correctly explain what the probability means. Now consider the question of how likely it is that at least one person in the room of 50 matches your particular birthday. (Do not attempt to calculate this probability.) Is this event more, less, or equally likely as the event that at least two people share any birthday? In other words, do you think this probability will be smaller than 0.97, larger than 0.97, or equal to 0.97 and why? Greater than 0.97 since your birthday is as likely to occur as any other. Equal to 9.97 since the probability has been determined previously. The probability cannot be predicted since we don't know how the people were selected to be in the room. Less than 0.97, since there are many pairs of people in the room that do not involve you and only 49 pairs of people that involve you.
Explanation / Answer
a)ans:
A likelihood esteem from an arbitrary test is the extent of times the occasion will happen over the long haul when the examination is rehashed.
For this situation, in straightforward terms, it implies how likely it is that atleast two individuals in the room comprising of 50 individuals have a similar birthday
b)ans:
This occasion is more probable when contrasted with the occasion that atleast two individuals share a similar birthday.
This is on account of possibility of two uncommon occasions occuring at the same time is lesser contrasted with shot of occurance of a solitary uncommon occasion (multiplicative lead in likelihood).
c)ans:
Reproduction can be utilized to affirm that the likelihood of the occasion that atleast two individuals share any birthday in a room comprising of 50 individuals is 0.97.
A cap contains 365 pieces of paper in it each with a number from 1 to 365 recorded on it.
Since there are 50 individuals in the room, every individual has 365 potential outcomes for a birthday.
Take the cap containing 365 slips on paper and number the slips from 1 to 365 (each number speaking to a specific day of the year).
Haphazardly pick 50 slips from the cap and note their numbers. This ought to be finished with substitution. It implies once the slip is taken out and its number noted, it ought to be returned to the cap for the second draw and soforth.
Change over the numbers to month and date.
Tally the quantity of occasions when a similar number is drawn more than once (slips in 50 attracts that relate to same month and date). .
This whole exercise ought to be rehashed a few times to affirm the likelihood (0.97)
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