Bill and Ben each have three cards numbered 4,5,6 they each take one of their own cards then they add the two numbers on the cards what is the probability that their answer is an odd number. What is the probability that their answer is a number less than 11.

Step-by-step explanation:

There are 9 possible outcomes for (Bill, Ben)'s cards:

  (4, 4) total 8; (4, 5) total 9; (4, 6) total 10;

  (5, 4) total 9; (5, 5) total 10; (5, 6) total 11;

  (6, 4) total 10; (6, 5) total 11; (6, 6) total 12.

Of these 9 outcomes, 4 have an odd total; 6 are less than 11.

 P(odd) = 4/9

  P(sum < 11) = 2/3

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: