Answer:
(a)
The probability that you stop at the fifth flip would be

(b)
The expected numbers of flips needed would be

Therefore, suppose that
, then the expected number of flips needed would be 1/0.5 = 2.
Step-by-step explanation:
(a)
Case 1
Imagine that you throw your coin and you get only heads, then you would stop when you get the first tail. So the probability that you stop at the fifth flip would be

Case 2
Imagine that you throw your coin and you get only tails, then you would stop when you get the first head. So the probability that you stop at the fifth flip would be

Therefore the probability that you stop at the fifth flip would be

(b)
The expected numbers of flips needed would be

Therefore, suppose that
, then the expected number of flips needed would be 1/0.5 = 2.
The probability that one of each color is selected is 
<h3>Probabilities</h3>
The probability of an event is the chances of the said event
The given parameters are:
- Total = 10
- Red = x
- Blue = 10 - x
<h3>Calculating the required probability</h3>
The probability that one of each color is selected is calculated as follows:

So, we have:

This gives

Take LCM

Simplify the above expression

Expand

Hence, the probability that one of each color is selected is 
Read more about probabilities at:
brainly.com/question/7965468
$89$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Answer:
In the equation, it divides 21 by x before knowing what x is, and gets it incorrect. Instead, you need to divide 21 by -4.2.
Step-by-step explanation:
-4.2x = 21
-------------
-4.2
x = -5