A dice is thrown two times and the total throw is noted. Find the probability that the total score is       1. Even no.     2. Six      3.  Less than 10.

Asked by arpitt682 | 2nd Mar, 2020, 05:35: AM

Expert Answer:

A die is thrown two times
T o t a l space o u t c o m e s equals left curly bracket left parenthesis 1 comma 1 right parenthesis comma space left parenthesis 1 comma 2 right parenthesis comma space left parenthesis 1 comma 3 right parenthesis comma space left parenthesis 1 comma 4 right parenthesis comma space left parenthesis 1 comma 5 right parenthesis comma space left parenthesis 1 comma 6 right parenthesis comma left parenthesis 2 comma 1 right parenthesis comma... comma left parenthesis 2 comma 6 right parenthesis comma left parenthesis 3 comma 1 right parenthesis comma... comma left parenthesis 3 comma 6 right parenthesis comma left parenthesis 4 comma 1 right parenthesis comma... comma left parenthesis 4 comma 6 right parenthesis comma left parenthesis 5 comma 1 right parenthesis comma... left parenthesis 5 comma 6 right parenthesis comma left parenthesis 6 comma 1 right parenthesis comma... comma left parenthesis 6 comma 6 right parenthesis right curly bracket
T o t a l space n o. space o f space o u t c o m e s space equals space 36
1. space E v e n space n o.
F a v o r a b l e space o u t c o m e s equals space left curly bracket left parenthesis 1 comma 1 right parenthesis comma space left parenthesis 1 comma 3 right parenthesis comma space left parenthesis 1 comma 5 right parenthesis comma space left parenthesis 2 comma 2 right parenthesis comma space left parenthesis 2 comma 4 right parenthesis comma space left parenthesis 2 comma 6 right parenthesis comma space left parenthesis 3 comma 1 right parenthesis comma space left parenthesis 3 comma 3 right parenthesis comma space left parenthesis 3 comma 5 right parenthesis comma space left parenthesis 4 comma 2 right parenthesis comma space left parenthesis 4 comma 4 right parenthesis comma space left parenthesis 4 comma 6 right parenthesis comma space left parenthesis 5 comma 1 right parenthesis comma space left parenthesis 5 comma 3 right parenthesis comma space left parenthesis 5 comma 5 right parenthesis comma space left parenthesis 6 comma 2 right parenthesis comma space left parenthesis 6 comma 4 right parenthesis comma space left parenthesis 6 comma 6 right parenthesis right curly bracket
N o. space o f space f a v o r a b l e space o u t c o m e s equals 18
P r o b a b i l i t y equals 18 over 36 equals 1 half

2. space S i x
F a v o r a b l e space o u t c o m e s equals left curly bracket left parenthesis 1 comma 5 right parenthesis comma space left parenthesis 2 comma 4 right parenthesis comma space left parenthesis 3 comma 3 right parenthesis comma space left parenthesis 4 comma 2 right parenthesis comma space left parenthesis 5 comma 1 right parenthesis right curly bracket
N o. space o f space f a v o r a l e space o u t c o m e s equals 5
P r o b a b i l i t y equals 5 over 36

3. space L e s s space t h a n space 10
F a v o r a b l e space o u t c o m e s equals left curly bracket left parenthesis 1 comma 1 right parenthesis comma space left parenthesis 1 comma 2 right parenthesis comma space left parenthesis 1 comma 3 right parenthesis comma space left parenthesis 1 comma 4 right parenthesis comma space left parenthesis 1 comma 5 right parenthesis comma space left parenthesis 1 comma 6 right parenthesis comma space left parenthesis 2 comma 1 right parenthesis comma space left parenthesis 2 comma 2 right parenthesis comma space left parenthesis 2 comma 3 right parenthesis comma space left parenthesis 2 comma 4 right parenthesis comma space left parenthesis 2 comma 5 right parenthesis comma space left parenthesis 2 comma 6 right parenthesis comma space left parenthesis 3 comma 1 right parenthesis comma space left parenthesis 3 comma 2 right parenthesis comma space left parenthesis 3 comma 3 right parenthesis comma space left parenthesis 3 comma 4 right parenthesis comma space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis 3 comma 5 right parenthesis comma space left parenthesis 3 comma 6 right parenthesis comma space left parenthesis 4 comma 1 right parenthesis comma space left parenthesis 4 comma 2 right parenthesis comma space left parenthesis 4 comma 3 right parenthesis comma space left parenthesis 4 comma 4 right parenthesis comma space left parenthesis 4 comma 5 right parenthesis comma space left parenthesis 5 comma 1 right parenthesis comma space left parenthesis 5 comma 2 right parenthesis space left parenthesis 5 comma 3 right parenthesis comma space left parenthesis 5 comma 4 right parenthesis comma space left parenthesis 6 comma 1 right parenthesis comma space left parenthesis 6 comma 2 right parenthesis comma space left parenthesis 6 comma 3 right parenthesis right curly bracket
N o. space o f space f a v o r a b l e space o u t c o m e s equals 30
P r o b a b i l i t y equals 30 over 36 equals 5 over 6

Answered by Renu Varma | 2nd Mar, 2020, 10:32: AM