Fran has a fair coin that has the numbers 0 written on one s

Fran has a fair coin that has the numbers 0 written on one side and 1 written on the other. Ron has a computer that generate random number that are uniformly distributed between 0 and 1. Fran tosses her coin and Ken generates a random number .

1- Find the probability that the sum of Fran\'s number is greater than Ron\'s number.
2-Find the expected Value of the sum of Fran\'s number plus Ron\'s number.
3-Find the probability that the sum of fran\'s number plus Ron\'s number lies between 0.9 and 1.8.

Solution

sum frans number= 0+1 = 1

sums rons number =0+0.1+0.2+0.3+0.4+0.5+0.6+0.7+0.8+0.9+1=5.5

Frans Number

P(X) for 0-----------0.5

P(x) for 1-------------0.5

Rons numbers Probability

0-----------1/11

0.1-----------1/11

0.2-----------1/11

0.3-----------1/11

0.4-----------1/11

0.5-----------1/11

0.6-----------1/11

0.7-----------1/11

0.8-----------1/11

0.9-----------1/11

1-----------1/11

1)

Probability that sums of frans number is greater than rons numbers

0.5*(5*1/11) / 1+1 = 0.1136

2)

expect value

For number fran 0

0-----------1/11-------0*1/11=0

0.1-----------1/11-----0.1*1/11=0.009

0.2-----------1/11-----0.2*1/11=0.018

0.3-----------1/11-----0.3*1/11=0.027

0.4-----------1/11-----0.4*1/11=0.036

0.5-----------1/11-----0.5*1/11=0.045

0.6-----------1/11-----0.6*1/11=0.054

0.7-----------1/11-----0.7*1/11=0.0636

0.8-----------1/11-----0.8*1/11=0.0727

0.9-----------1/11-----0.9*1/11=0.0818

1-----------1/11-----1*1/11=0.09

sums=

0.009+0.018+0.027+0.036+0.045+0.054+0.0636+0.0727+0.0818+0.09=0.498

Part of the expect value 0.498*2 = 0.996