Intro to Probability Question I'm stucked in two problems: 2. Suppose that a 1-meter glass rod falls onto the floor and is broken into two pieces. Assume that the breaking point is uniform between 0 and 1 meter. What is the probability that the longer piece has length at least 0.6 meter? **I have solved this one but I don't think it's correct** Please look at the picture. I draw a line x+y=1 and then find the area of where x>=6. And then solve the area of the trangle which is 1/2*0.4*0.4=0.08 5. I solved i) but have no idea for ii). Please see picture attached. Question image Thank you so much ahead!

Suppose $Z$ is the distance between the breaking point and one end point of your rod. Then Z~U(0,1)

So P(The longer piece has length at least 0.6 meter)=

$P(Z>0.6$ or $Z<0.4)=P(Z>0.6)+P(Z<0.4)=(1-0.6)+(0.4)=0.8$, that's the answer of you question.

Notice that you cannot use two dimension plot to help you solve this problem because X and Y are correlated, there is no way to solve it by this kind of plot.

5ii:

You should first show that in order to prove 5ii, you need to prove:

$P(AB)+P(BC)-P(AC)
Hint:using 5i to expand every item.

Then you should know $P(A\cup B)=P(A)+P(B)-P(AB)$

Try to expand $P\\{(AB)\cup (BC)\\}$ and prove $P(AB)+P(BC)-P(AC)