You are not logged in.
Pages: 1
Hi, this is the word problem I was given:
"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)."
Let me try to explain my position. I can't quite remember the formula for how to compute this. I gather a Venn-Diagram might be of some assistance. So I put the 0.2 in one circle, 0.04 in the intersection and 0.1 in the other circle. So there's my Venn-Diagram, but I just don't know what to do with the numbers once they're in their respective circles.
Another thing on which I'm confused: Why isn't the answer 0.66? Don't probabilities have to = 1, in other words 100%? AND if the answer's not .66, if it's anything other than .66, let's just say it's .26, for example—just as an example!—then your front light breaks down is .2, your back light breaks down is 0.1, they both fail is 0.04, and they both work is 0.26 (again, just an example), all of which adds up to .6. So what's happening the other 40% of the time you ride the bike? Something has to be happening?
In helping me, please don't just give me the answer. Please respond specifically to what I wrote above. Please tell me, now that I explained my line of thinking, where I am going wrong. That's the only way I can really learn it. And a little patience, if you will. As you can see, I'm not very good at this. Thank you.
Your answer is correct. In probability the "sample space" should equal to "1" since it contains all the possible outcomes. In the problem, which you stated, the sample space has been provided except one possiblity which is "that both lights work" hence if we call the chance that both lights work "x" we will have:
0.2+0.1+0.04+x=1 ⇒ x=1-0.34=0.66
In this case the probability of any one of them to occur is 100%. I think that answer your question.
Offline
Pages: 1