- because we're dealing with circles, we'll be dealing with the area and where we want to hit and where all the possible places are to hit.
- Keep in mind that the favorable outcome is the bullseye but the person doesn't have to hit the bullseye with the whole arrow, only a portion of it has to hit. So, Sebastian's farvorable area to hit would be everything within the blue circle because the farthest the arrow could be would be just hitting the outer cicumference of the bullseye and that would count.
- By using the radii of the two circles we have an area that is favored for the arrow to hit. We can than apply the same concepts to the outer edge of the target and we can continue our calculation.
- The radius of the first one would be 2 cm because the bullseye's diametre is 3 cm, the radius of the bullseye would be 1.5 cm. The diameter f the shaft of the arrow is 1 cm, the radius of the shaft must be 0.5 cm. Together the radii make the favorable arrow because that's where Sebastian can hit to get a bullseye. That's divided by all possible outcomes which is π(15.5)² because the diameter of the whole target is 30 cm, which must mean that the radius is 15.5 cm. The pi's reduce.
- Sebastian has to nick his own arrow and this uses the same logic. The radius of the arrow that his trying to hit is .05 cm and his own arrow is 0.5 cm, which gives us a radii of 1 cm together. Sebastian's favorable outcome is π(1)². All possible outcome is still the same because he can hit anywhere else on the target which is π(15.5)².
- Then to find the probability of this happening one arrow after the other, multiply the probabilities together.
- Sebastian's probability of splintering his own arrow that he's trying to send into the bullseye is:
- Which is really really small. However, that's the chance that everyone has as well. In the end no one got it so everyone decided to go out and eat.
- Keep in mind that the favorable outcome is the bullseye but the person doesn't have to hit the bullseye with the whole arrow, only a portion of it has to hit. So, Sebastian's farvorable area to hit would be everything within the blue circle because the farthest the arrow could be would be just hitting the outer cicumference of the bullseye and that would count.
- a closer view of Sebastian's favorable area. The favorable area would be the bullseye area plus the whole area that the arrow can land around it while sitting on it.
- By using the radii of the two circles we have an area that is favored for the arrow to hit. We can than apply the same concepts to the outer edge of the target and we can continue our calculation.
- The radius of the first one would be 2 cm because the bullseye's diametre is 3 cm, the radius of the bullseye would be 1.5 cm. The diameter f the shaft of the arrow is 1 cm, the radius of the shaft must be 0.5 cm. Together the radii make the favorable arrow because that's where Sebastian can hit to get a bullseye. That's divided by all possible outcomes which is π(15.5)² because the diameter of the whole target is 30 cm, which must mean that the radius is 15.5 cm. The pi's reduce.
- Sebastian has to nick his own arrow and this uses the same logic. The radius of the arrow that his trying to hit is .05 cm and his own arrow is 0.5 cm, which gives us a radii of 1 cm together. Sebastian's favorable outcome is π(1)². All possible outcome is still the same because he can hit anywhere else on the target which is π(15.5)².
- Then to find the probability of this happening one arrow after the other, multiply the probabilities together.
- Sebastian's probability of splintering his own arrow that he's trying to send into the bullseye is:
- Which is really really small. However, that's the chance that everyone has as well. In the end no one got it so everyone decided to go out and eat.
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