Question

A fair six-sided dice is thrown and the scores are noted.

Event X: The total of the two scores is 4.

Even Y: The first score is 2 or 5.                                       

b)             Find the probability of X and Y.                                                                        

Answer 1

A dice is thrown two times. So, total outcomes = $6^2=36.$

Event X: The total of the two scores is 4

$$(1,3), (2,2), (3,1)$$

$$P(X)=\dfrac{3}{36}=\dfrac{1}{12}$$

Event Y: The first score is 2 or 5

$$(2,1), (2,2), (2,3),(2,4), (2,5), (2,6),$$

$$(5,1), (5,2), (5,3),(5,4), (5,5), (5,6),$$

$$P(Y)=\dfrac{12}{36}=\dfrac{1}{3}$$