Probability of Power Rangers, please correct me if I am wrong There are five Power Rangers.  Of the five,  two are male(Red, Black) and three are female (Pink, Yellow,blue.)I randomly select two of the Power Rangers, without replacement.
(a)  What is the probability that the black Ranger is one of the two selected Power Rangers?
pretending that you only randomly select one power ranger, the 
probability of picking the black would just be 1/5, so if you were 
to pick another it would be 1/4 so it would be 1/5 * 1/4 = .05 so 5% chance? 
it just seems low

(b)  What is the probability at least one of the two selected Power Rangers is female?
probability that one is female is 3/5, so if you were to pick 
another power ranger at random would it be 3/5*3/4

(c)  Given that at least one of the two selected Power Rangers is male, what is the conditional probability the Pink Ranger is selected?
conditional probability, wouldnt it just be 33.3% that the pink is selected given theres only three females?

(d)  Are the events “the Pink Ranger is one of the two selected” and “at least one of the two selected Power Rangers is female” independent?  Explain why or why not.
Yes, event A effects event B. 


 A: As the commenters have pointed out, your intuition to doubt your answer to (a) was appropriate.
$$
P(\text{selected Pink}) = P(\text{Pink selected first}) + P(\text{Not pink, then Pink}) = 1/5 + 4/5 \times 1/4 = 2/5.
$$
Then
$$
P(\text{At least } 1 \text{ female}) = 1 - P(\text{both male}) = 1 - 3/5 \times 2/4 = 1 - 3/10 = 7/10.  
$$
Next, use Bayes's Theorem:
$$
P(\text{Pink}|\text{At least 1 female}) = \frac{P(\text{Pink AND at least 1 female})}{P(\text{At least 1 female})} = \frac{P(\text{Pink})}{P(\text{At least 1 female})} = \frac{2/5}{7/10} = \frac{4}{7}. 
$$
(Can you see why the middle equality is true? This is useful in the final part!)
Finally, recall that two events $A,B$ are independent if $P(A \cap B) = P(A)P(B)$. Can you use this to give a clearer explanation for (d)?
A: As an alternative to directly using probabilities, Bayes' Theorem, etc., the way I personally think about these questions is first through counting. And then at the end as the last step, perform a division to get the probability. I find that this helps to avoid thinking about "first" make a selection and "second" make a different selection, and all the traps my brain could fall into when thinking that way.
With 5 people to choose 2 from, there are $\binom{5}{2}=\frac{5\cdot4}{2!}=10$ ways to just choose 2 people, regardless of one being pink or not, or whatever. These 10 possible pairs are all equally likely.
How many pairs of 2 people do have the pink ranger? Easy, that's just 4 since you have 4 options for who pink's partner would be.
So out of 10 equally likely possible pairs, 4 qualify. The probability is $\frac{4}{10}$.
For (b), how many pairs have one or more females? Well, how many possible pairs are all male? That's $\binom{3}{2}=\frac{3\cdot2}{2!}=3$. So $7$ of the pairs have at least one female, and the probability is $\frac{7}{10}$.
I don't want to continue laying out answers to (c) and (d). But do you see how to apply the same process to understand an answer for (c)?
