Carol constructed a cube and marked each face with a number.
She marked the faces with the numbers 1, 2, 2, 3, 3, and 4. If she
rolls the cube twice, what is the probability that the sum of the
numbers will be exactly 7?

9514 1404 393

  1/9

Step-by-step explanation:

Carol can roll a total of 7 in two ways: 3 +4 or 4 + 3.

Two of the six faces are marked with 3, so the probability of rolling a 3 is 2/6 = 1/3. One of the six faces is marked with 4, so the probability of rolling a 4 is 1/6.

Then the probability of rolling a 3, then 4 is (1/3)(1/6) = 1/18. Similarly, the probability of rolling a 4, then 3 is (1/6)(1/3) = 1/18. These are presumed independent so the probability of one or the other of these outcomes is ...

  1/18 +1/18 = 1/9

The probability that the sum is exactly 7 after two rolls is 1/9.

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²