(1) What is the greatest number of points of intersection that can occur when 2 different circles and 2 different straight lines are drawn on the same piece of paper?

(2) Let p be a prime number between 40 and 60. What is the probability that p+12 is also a prime number? Express your answer as a common fraction

tertre
Dec 3, 2017

#1**+1 **

(1) I believe the answer to this is 11

The circles can intersect at 2 points

Each line can intersect each circle twice = 8 points

And as long as the lines do not intersect at any of the other points, they can intersect at 1 additional point

(2) Primes between 40 and 60 are

41 , 43 , 47, 53 , 59

And adding 12 to these =

53 , 55 , 59, 65 , 71

And 3 out of the 5 are prime [ 53, 59, 71 ]

So....the probability that p + 12 is prime is 3 / 5

CPhill
Dec 3, 2017