An Moment When No one was watching

You must have a few secretes of your own, it might be some activity or an hobby that you enjoy to do but you don’t want anyone not even your closest friend to find out with whom you had done man grave sins. to plan such an action you will need an time period to execute your business, Then the question comes what is the best time to do your secret thing

this Leads to another interesting Question : Has there ever been an moment in our entire human history that no one was watching because it just so happens that everyone blinked at the same time, Lets deep dive into this question with the help of math

Involved Variables

You need to know about these to solve this problem,

Blinking is a bodily function; it is a semi-autonomicr apid closing of the eyelid A single blink is determined by the forceful closing of the eyelid or inactivation of the levator palpebrae superioris and the activation of the palpebral portion of the orbicularis oculi, not the full open and close It is an essential function of the eye that helps spread tears across and remove irritants from the surface of the cornea and conjunctiva.

On average, most people blink around 15 to 20 times every minute. This adds up to nearly 14,000 to 20,000 blinks every single day. Blinking is constant, but we hardly notice it because it happens so fast.

• An Normal Human Blink is about 1/3 of a second
• An Normal Human Blinks once in every 4 second

Probability of an Blink

At an given moment an given person has an probably that that person is blinking is 1/12, You can get to this result by some basic concepts,

• 1 Blink takes 1/3 second , lets take it as ‘x’ then how many ‘x’ are there in 4 second , 1 second has 3x then 4 second has 12x
• Finding the probability ( Number of Favorable Outcomes / Total number of outcomes ), in 4 second an person only blinks once therefore there is only ONE Favorable Outcomes. Thus the probability becomes 1/12

Conclusion : At an Given instance of time the probability of an person blinking ( having his eyelids closed ) is 1/12

Scaling it for ’n’ number of persons

To find the probability of say 2 persons blinking at the same time will be 1/12 * 1/12 its only logical to conclude this, because as the number of persons increase the probably of an simultaneous blink decreases in addition to this these are two separate and independent events allowing us to use the general probability rules

By this We can draw an general formula for ’n’ number of persons. The Probability of an simultaneous blink would be,

P(E) = 1/12^n

Figuring Out the time period

At the beginning we assumed x=1/3 seconds and thus got the probability of 1/12 to be precise 1x/12x how can we relate this to time,We simply need to find the value of “12^n times x” by substituting the value of x =1/3 the result will give us time in seconds