Question

Take a stick and break it into two pieces, choosing the break point at random from a uniform distribution. What is the probability that the larger piece is no more than 5.7 times as long as the smaller piece?

Answer 1

Answer:

0.701

Step-by-step explanation:

let y be the length of the larger stick piece and 1-y, the length of the smaller piece.

y/1-y < 5.7

y< 5.7/6.7

when y is seen from the left side

1-y/y <5.7

y> 1/6.7

multiplying both by 10

y<57/67 and y>10/67

therefore probability is

10/67 < y < 57/67

57-10/67

= 47/67

=0.701