Answer to Question #174699 in Statistics and Probability for faisal

Question

Two fair dice are thrown, one red and one blue. What is the

probability that the red die has a score that isstrictly greater

than the score of the blue die? Why is this probability

less than 0.5? What is the complement of this event?

Answer 1

Solution:

Two dice are there, red and blue.

$n(S)=6^2=36$

Let E be the event of getting greater number on red die.

{a,b}, where a represents number appeares on red die and b that on blue die.

$E=\{(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),\\(5,4),(6,1),(6,2),(6,3),(6,4),(6,5)\}$

$n(E)=15$

Now, $P(E)=\frac{15}{36}=\frac{5}{12}$

It is $\frac5{12}<0.5$ because we took numbers strictly greater than on red die.

Now, $P(E')=1-P(E)=1-\frac5{12}=\frac7{12}$