Question

From a group of 13 scientists which contain 5 mathematicians and 8 physicists, it is required to appoint a committee of two. if the selection is made without knowing the identity of the scientists, what is the probability that one will be mathematician and the other a physicist?

Answer 1

Probability =(13c1+8c1)/21c2
Hope it helps.......

Answer 2

Answer:

From a group of 13 scientists we have to select a committee of two so (132)=78

From 5 mathematician we can form a committee of two (52)=10

From 8 physicist we can form a committee of two (82)=28

Since we want one mathematician and one physicist in committee of two =78−10−28=40

so i guess 40 combination of a committee with one mathematician and one physicist can be formed out 78 combination.

Therefore the P(1Math and 1Physicist)=(4078)=(2039)

Step-by-step explanation: STEP :1 If you take someone at random 813 it's a physicist and at the second pick 512 a mathematician, in the other way 513 a mathematician and 812 a physicist.

$813512+513812=2039$

$(81)(51)(132)=1−(51)(132)−(52)(132)=813⋅512+513⋅812$

STEP: 2Generally mathematicians and physicists speak the same language. We study each other’s fields, even if we both have a different focus. Though in my experience a typical physicist’s comment to a mathematician is “Can you dumb that down a bit for me?”, and a typical mathematician’s comment to a physicist is “You are not allowed to do that!”

My favorite story along these lines: Paul Dirac, one very smart physics dude, invented the “Dirac delta function”. This is a function that is zero everywhere but infinity at a single point, and that also has a definite integral of 1, i.e. under the single infinite point there is an area of 1. The use of this function is immediately obvious to anyone studying electrodynamics, or more generally Green’s functions in differential equations. However, mathematicians looked at this construction and immediately said, “That is ill-defined! How can you have one point at infinity with an area under it of 1?” Some years later mathematicians came up with the idea of “distribution” - an object that only exists inside an integral, and is something one integrates a function over.

(Now that I think about this, it must be closely related to measure theory and Lebesgue integration. But that is why you study real analysis.)

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