Addition Rule / Probability

Question

1996: There were 737,764 physicians in the USA, and 157,387 of them were female.

There were 133,005 physicians under 35 years of age, and 47,348 of them were female.

 

What is the probability that a randomly chosen physician in 1996 was female or under the age of 35?

Answer 1

Hi Christopher,

 

               Under 35          Other Age     Total

 

 

Females    47,348            110,039       157,387

 

 

Males       85,657             494,720        580,377  

 

 

Total       133,005            604,759        737,764

 

F: Event that a randomly chosen physician in 1996 was female

Y: Event that a randomly chosen physician in 1996 was under the age of 35

P(FUY) = P(F)  + P(Y) - P(F∩Y)

          =(157,387/737,764) + (133,005/737,764) - (47,348/737,764)

          =243,044/737,764

The probability that a randomly chosen physician in 1996 was female or under the age of 35 ~0.329433

 

Answer 2

P[A∪B] be physicians under 35 or female

P[A] be total female physicians in usa

P[B] be physicians under 35 in usa

P[A∩B] be physicians under 35 and female

 

P[A∪B] = P[A] + P[B] - P[A∩B]

P[A] = 157387/737764 = 0.213

P[B] = 133005/737764 = 0.180

P[A∩B] = 47348/737764 = 0.07

P[A∪B] = 0.323