8. suppose in a certain breed of dog, the color of fur can either be tan or black. eighty-five percent of the time, a puppy will be born with tan fur, while 15% of the time, the puppy will have
black fur. suppose in a future litter, six puppies will be born.
a. are the events having tan fur and having black fur independent? explain.
b. what is the probability that one puppy in the litter will have black fur and another puppy will have tan fur?
c. what is the probability that all six puppies will have tan fur?
d. is it likely for three out of the six puppies to be born with black fur? justify mathematically.

a) On this case the two events are independent, because if one puppy is black the probability that the next one would be black or tan fur is not affected by the first outcome. On math terms we have this:

b) On this case since the order no matter the probability would be:

And the two events are independent.

c) For this case the probability that all six puppies will have tan fur is:

d) On this case the probability that 3 puppies would be black fur means that the other 3 are tan fur. And the probability would be given by:

So on this case is very unlikely since we have just about 0.2% of possibility.

Step-by-step explanation:

Notation

T= a pupy is tan fur, P(T) = 0.85

B= a puppy is black fur P(B) = 0.15

a. Are the events having tan fur and having black fur independent? Explain.

On this case the two events are independent, because if one puppy is black the probability that the next one would be black or tan fur is not affected by the first outcome. On math terms we have this:

b. What is the probability that one puppy in the litter will have black fur and another puppy will have tan fur?

On this case since the order no matter the probability would be:

And the two events are independent.

c. What is the probability that all six puppies will have tan fur?

For this case the probability that all six puppies will have tan fur is:

d. Is it likely for three out of the six puppies to be born with black fur? Justify mathematically.

On this case the probability that 3 puppies would be black fur means that the other 3 are tan fur. And the probability would be given by:

So on this case is very unlikely since we have just about 0.2% of possibility.

125 yards

step-by-step explanation:

i take 75 plus 50.

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.