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Two buddies, Zeke and Bubba, plan a squirrel-hunting trip. Bubba is a better shot than Zeke. How much better? Bubba is 2 times a better shot than Zeke. Upon seeing a squirrel, Bubba and Zeke raise their rifles and simultaneously shoot at the squirrel. Assume that Bubba shooting the squirrel and Zeke shooting the squirrel are independent events, and that the probability of Zeke shooting the squirrel is 0.25.

Part (a) If the squirrel is shot, what is the probability that Zeke shot the squirrel?
\[ P(\text{Zeke shot the squirrel}) = \] (use four decimals)

Part (b) If only one of the two buddies shot the squirrel, what is the probability it was Bubba?
\[ 0.625 \] (use four decimals)

Answer :

Final answer:

To find the probability that Zeke shot the squirrel, we can use conditional probability and the provided information. The probability that Zeke shot the squirrel is approximately 0.3333. The probability that Bubba shot the squirrel is approximately 0.6667.

Explanation:

To find the probability that Zeke shot the squirrel, we can use the formula for conditional probability: P(Zeke shot the squirrel) = P(Zeke shot the squirrel and Bubba did not) / P(Only one of them shot the squirrel).

Based on the given information, the probability that Zeke shot the squirrel and Bubba did not is 0.25. The probability that only one of them shot the squirrel is equal to the sum of the probabilities that Zeke shot the squirrel and Bubba did not, and that Bubba shot the squirrel and Zeke did not. Since Bubba is 2 times better shot, the probability that Bubba shot the squirrel and Zeke did not is 2 * 0.25 = 0.5.

Therefore, P(Only one of them shot the squirrel) = 0.25 + 0.5 = 0.75.

So, P(Zeke shot the squirrel) = 0.25 / 0.75 = 0.3333 (rounded to four decimals).

For part (b), the probability that Bubba shot the squirrel can be calculated similarly. P(Bubba shot the squirrel) = P(Bubba shot the squirrel and Zeke did not) / P(Only one of them shot the squirrel).

The probability that Bubba shot the squirrel and Zeke did not is 0.5 (as calculated earlier). So, P(Bubba shot the squirrel) = 0.5 / 0.75 = 0.6667 (rounded to four decimals).

Learn more about Conditional Probability here:

https://brainly.com/question/32171649

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