2dice are tossed once what is the probability that the sum is less than 7

5/9

Step-by-step explanation:

To get the probability of getting a sum less than 7 from rolling two dice once, first one needs to draw the sample space for all the possible outcomes as shown below:

     1.       2.       3.       4.       5.      6.

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

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

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

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

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

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

There are 15 events (underlined) that give a sum less than 7 out of the total of 36 possible events in the sample space.

Probability =  Number of favorable outcomes

            Total number of possible outcomes

Pr(Sum less than 7) =       15/36

Pr(Sum less than 7) =        5/9

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2