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11Alexandr11 [23.1K]
2 years ago
9

Not sure how I would go about solving this problem. Any help would be appreciated

Mathematics
1 answer:
earnstyle [38]2 years ago
4 0
You can figure out that angle 5 equals 81 because 52 + 47 + 81 = 180, angle 4 = angle 5 (81) + 52 so angle 4 is 133 angle 1 is angle 5 (81) + 47 so angle 1 is 128. Knowing these angle 2 would be 52 and angle 3 would be 47

for simple answers

angle 1 = 128
angle 2 = 52
angle 3 = 47
angle 4 = 133
angle 5 = 81
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1. The table shows the probabilities of a response chocolate or vanilla when asking a child or adult. Use the formula for condit
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\begin{matrix}&\text{chocolate}&\text{vanilla}&\text{total}\\\text{children}&0.14&0.26&0.40\\\text{adults}&0.21&0.39&0.60\\\text{total}&0.35&0.65&1.00\end{matrix}

a. "Chocolate" and "Adults" (whatever those mean) will be independent as long as

P(\text{chocolate}\cap\text{adults})=P(\text{chocolate})\cdot P(\text{adults})

"Chocolate" has the marginal distribution given by the second column, with a total probability of P(\text{chocolate})=0.35. Similarly, "Adults" has the marginal distribution described by the third row, so that P(\text{adults})=0.60. Then

P(\text{chocolate})\cdot P(\text{adults})=0.35\cdot0.60=0.21

Meanwhile, the joint probability of "Chocolate" and "Adults" is given by the cell in the corresponding row/column, with P(\text{chocolate}\cap\text{adults})=0.21.

The probabilities match, so these events are indeed independent.

Parts (b) and (c) are checked similarly.

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P(\text{children})\cdot P(\text{chocolate})=0.40\cdot0.35=0.14
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c. Yes;

P(\text{vanilla})\cdot P(\text{children})=0.65\cdot0.40=0.26
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