Q:

Two fair dice are tossed, and the up face on each die is recorded. Find the probability of observing each of the following events: A:{ The difference of the numbers is 2 or less } B:{ A 4 does not appear on either die } C:{ The sum of the numbers is 10 or more }

Accepted Solution

A:
Answer:Step-by-step explanation:When two fair dice are tossed sample space consists of 36 events(1,1)....(6,6)A_ The difference of numbers is 2 or lessFavorable outcomes = [tex](1,1) (1,2) (1,3) (2,1) (2,2)(2,3) (2,4) (3,1) (3,2) (3,3) (3,4) (3,5) (4,2) (4,3)(4,5) (4,6) (5,3) (5,4) (5,6)\\[/tex]Hence Probability = [tex]\frac{19}{36}[/tex]B) A 4 does not appear on either dieThen we must not have these[tex](4,1)(4,2)(4,3) (4,4) (4,5) (4,6)\\(1,4) (2,4) (3,4) (5,4) (6,4)[/tex]Hence probability = [tex]\frac{36-11}{36} =\frac{25}{36}[/tex]C:  The sum of numbers is 10 or more:FAvourable outcomes are:[tex](4,6) (5,5) (5,6) (6,5) (6,4)[/tex]Probability = [tex]\frac{5}{36}[/tex]