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irga5000 [103]
3 years ago
5

The table shows whether members in a fishing group caught fish or did not catch fish and whether they fished from a boat or from

the shore. One member is randomly selected.
What is the probability that the members fished from a boat, given that he or she caught fish?
Write the probability as a percent. Round to the nearest tenth of a percent as needed.

Mathematics
2 answers:
SIZIF [17.4K]3 years ago
7 0

Answer: 64.9%

Step-by-step explanation:

From the given table , the number of members caught fish =24+13=37

Total Members = 24+11+13+8=56

Let A be the event that members caught fish , then

P(A)=\frac{37}{56}

Let B be the event of members fished from a boat.

The number of members fished from boat and caught fish = B\cap A=24

Then, P(B\cap A)=\frac{24}{56}

Now, the probability that the members fished from a boat, given that he or she caught fish is given by :-

P(B|A)=\dfrac{P(B\cap A)}{P(A)}\\\\=\dfrac{\dfrac{24}{56}}{\dfrac{37}{56}}\\\\\\=\dfrac{24}{37}=0.648648648649

In percent, P(B|A)= 0.648648648649\times100=64.8648648649\%\approx64.9\%

Hence, the probability that the members fished from a boat, given that he or she caught fish=64.9%

MariettaO [177]3 years ago
3 0
The given scenario falls under the category of conditional probability. There are a total of 56 people in the fishing group described above. The probability that the a person caught a fish and fished from a boat is 24/56. The probability that he fished from a boat is (24+11)/56. For the conditional probability in this item is,
                                 P = (24/56) / ((24+11)/56) = 24/35 = 0.69
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