A Starburst candy package contains 12 individual candy pieces. Each piece is equally likely to be berry, orange, lemon, or cherry, independent of all other pieces. (a) What is the probability that a Starburst package has only berry or cherry pieces and zero orange or lemon pieces

(a) Each piece is “berry or cherry” with probability p = 1/2. The proba-

bility of only berry or cherry pieces is p

12 = 1/4096.

Step-by-step explanation:

(b) Each piece is “not cherry” with probability 3/4. The probability all 12

pieces are “not pink” is (3/4)12 = 0.0317.

(c) For i = 1, 2, . . . , 6, let Ci denote the event that all 12 pieces are flavor i.

Since each piece is flavor i with probability 1/4, P[Ci

] = (1/4)12. Since

Ci and Cj are mutually exclusive,

P[F1] = P[C1 ∪ C2 ∪ · · · ∪ C4] = X

4

i=1

P[Ci

] = 4 P[C1] = (1/4)11

.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

answer: bea's uncle is 25 years old.

step-by-step explanation:

given the equation , we can say that the variable "x" represents the age of bea's uncle. then to find his age, we need to solve for "x":

we must add 15 to both sides of the equation:

now we need to divide both sides of the equation by 3:

therefore, we can conclude that bea's uncle is 25 years old.