Question

(Please describe each solution step in detail.)

When we roll a pair of balanced dice, what are the probabilities of getting;

a) 7 ; b) 11 ; c) 7 or 11 ;   d) 3 ;   e) 2 or 12 ; f) 2, 3, or 12 ?

Answer 1

When we roll a pair of balance dice what are the probabilities of getting ;

=> Solution -:

Given data -

a) 7 -

= Number of ways to roll a 7 are (1,6) (2,5) (3,4) (4,3) (5,2) (6,1) = 6 ways

Total number of ways 62 = 36

P(Getting 7) = 6/36 = 0.1666

b) 11 -

= number of ways to roll 11 are (5,6) (6,5) = 2 ways

Total number of ways = 62 = 36

P( Getting 11) = 2/36 = 0.0555

c) 7 or 11 -

= number of ways getting 7 are 6 and number of ways of getting 11 are 2

Therefore number of ways getting 7 or 11 are 6+2 = 8 ways.

Total number of ways = 62 = 36

P ( Getting 7 or 11) = 8/36 = 0.2222

d) 3 -

= number of ways of getting 3 are (1,2) (2,1) = 2 ways

Total number of ways = 62 = 36.

P ( Getting 3 )= 2/36 = 0.0555

e) 2 or 12 -

= number of ways getting 2 are (1,1) =1 way.

Number of ways getting 12 are (6,6) = 1 way

Number of ways getting 2 or 12 = 1 + 1 = 2 ways.

Total number of ways = 62 = 36.

P ( Getting 2 or 12 ) = 2/36 = 0.0555

f ) 2 , 3 or 12 -

= number of ways of getting 2 , 3 or 12 =

1 + 2 + 1 ways = 4 ways

Total number of ways = 62 = 36.

P ( Getting 2 , 3 or 12) = 4/36 = 0.1111