Stats Word Problem2: chance that the front light on your bike will fail is 0.2

I

Idonotknowmath

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The chance that the front light on your bike will fail is 0.2, the chance that your rear light will fail is 0.1 and the chance that both will fail is 0.04. What is the chance that both lights will work? (regardless of the answer you should do something about this situation of course).
Give your answer as a proportion, rounding to two decimal places.

This is odd … because I think the question itself might actually be wrong. Isn't the chance they both fail 0.02, not 0.04? Either way, I think I have about 0.00 probability of figuring this out. If the chance that the one light will fail is 0.2 and the chance the other one will is 0.1, aren't you only looking for the remaining probability at that point (0.7)? Or 0.2, 0.1, & 0.02 leaves 0.68?

But it can't be that easy …

Can someone point me in the right direction? Ty.
 
Idonotknowmath said:
The chance that the front light on your bike will fail is 0.2, the chance that your rear light will fail is 0.1 and the chance that both will fail is 0.04. What is the chance that both lights will work? (regardless of the answer you should do something about this situation of course).
Give your answer as a proportion, rounding to two decimal places.

This is odd … because I think the question itself might actually be wrong. Isn't the chance they both fail 0.02, not 0.04? Either way, I think I have about 0.00 probability of figuring this out. If the chance that the one light will fail is 0.2 and the chance the other one will is 0.1, aren't you only looking for the remaining probability at that point (0.7)? Or 0.2, 0.1, & 0.02 leaves 0.68?

But it can't be that easy …

Can someone point me in the right direction? Ty.
Click to expand...

Draw Venn diagram:

Chance of failure of front light = 0.16 + 0.04

Chance of failure of rear light = 0.06 + 0.04

Now continue....
 
Idonotknowmath said:
The chance that the front light on your bike will fail is 0.2, the chance that your rear light will fail is 0.1 and the chance that both will fail is 0.04. What is the chance that both lights will work? (regardless of the answer you should do something about this situation of course).
Give your answer as a proportion, rounding to two decimal places.

This is odd … because I think the question itself might actually be wrong. Isn't the chance they both fail 0.02, not 0.04? Either way, I think I have about 0.00 probability of figuring this out. If the chance that the one light will fail is 0.2 and the chance the other one will is 0.1, aren't you only looking for the remaining probability at that point (0.7)? Or 0.2, 0.1, & 0.02 leaves 0.68?

But it can't be that easy …

Can someone point me in the right direction? Ty.
Click to expand...
Let (x,y)=(front light, rear light), F=fail, L=Light. The four possibilities we have are
Front Fails, Rear Fails = (F, F)
Front Fails, Rear Lights = (F, L)
Front Lights, Rear Fails = (L, F)
Front Lights, Rear Lights = (L, L)

We are given the following
Front Fails = (F, F) + (F, L) = 0.20
Rear Fails = (F, F) + (L, F) = 0.01
Both Fail = (F, F) = 0.04


Can you continue from there?
 
Idonotknowmath said:
The chance that the front light on your bike will fail is 0.2, the chance that your rear light will fail is 0.1 and the chance that both will fail is 0.04. What is the chance that both lights will work?
Click to expand...

\(\displaystyle 0.2+0.1-0.04=~?\) is the probability that at least one of the lights will fail.

What is the chance that both lights will work?
 
No, I'm pretty confused …

Is there a formula I should be using?

And if we have .2, and .1, and .04, and there's only one other option left, then how is the answer not .66 … given that all probabilities must equal 100%?
 
Idonotknowmath said:
Can anyone out there help me? And also explain how I went wrong in my previous replies? Ty.
Click to expand...
You've been given explanations of why and how to find the probability that one or the other (or both) of the lights fail. You've been told that this leads immediately to the probability that neither light fails (that is, that both lights work). What have you done with this information?

Please be complete. Thank you! ;)
 
Idonotknowmath said:
Can anyone out there help me? And also explain how I went wrong in my previous replies? Ty.
Click to expand...
Let's look at what you said:
"Isn't the chance they both fail 0.02, not 0.04?"
No, you are given that both will fail with probability 0.04

"Either way, I think I have about 0.00 probability of figuring this out."
If you don't pay attention to the posts trying to help you, I believe you are correct.

"If the chance that the one light will fail is 0.2 and the chance the other one will is 0.1, aren't you only looking for the remaining probability at that point (0.7). Or 0.2, 0.1, & 0.02 leaves 0.68?"
No and that may be your major problem. The 'independent probabilities' are for ordered pairs such as both fail (one case), only one fails (two cases, either front or back but not both), neither fails. You can draw a Venn diagram or just write down the numbers. From that you can determine what is needed and how to answer the question.
 
It's like you're just giving me the answer and not telling me why (and also why I'm wrong). That's not how I learn.

"You can draw a Venn diagram or just write down the numbers. From that you can determine what is needed and how to answer the question." I can draw the diagram and still not know what to do with the numbers once they're in their correct circles. My main problem is I don't know why they don't add up to 1? 0.2 + 0.1 - 0.04 = 0.26. Those are the 4 possible outcomes. Those add up to 0.6. So where's the 0.4? What's happening the other 40% of the time you ride the bike?

I expected the people trying to help me to have a little more paitence in doing so …
 
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