/--- 80% --- Red
/--/
/---\
/ \--- 20% --- Carmine
50%
---/
-_- (you blindfolded)
---\
50%
\ /--- 20% --- Red
\---/
\--\
\--- 80% --- Amaranth
You've got a $50\%$ chance of going up. At that point you have an $80\%$ chance of scoring Red. Good thing you're blindfolded, otherwise you might mistake Carmine for Red. Anyways, what's the probability of you following this path and hitting red?
$$
P(\text{up and red}) = 0.5 \cdot 0.8 = 0.4
$$
What about going down? Well, since you're not given the chance of mistaking Amaranth for Red (I really hope no one knows what Amaranth looks like), the math is pretty much the same.
$$
P(\text{down and red}) = 0.5 \cdot 0.2 = 0.1
$$
Since you're equally like to go both ways your probabilities add up. Thus you end up with
$$
P(\text{red}) = 0.4 + 0.1 = 0.5
$$
Save for the confusing colors and color names this should not seem too misleading. Good luck playing the game. I hope they give you good odds.
self-study
tag? Thank you. Why do you think your result is misleading? $\endgroup$