# Tutor profile: Erica T.

## Questions

### Subject: Mandarin

Translate the following sentence into Chinese: I want to go to Xiao Ming's house this Wednesday to play ball, but it looks like it will rain that day.

Simplified Chinese: 我这个星期三想去小明的家打球，可是那天看起来会下雨。 Traditional Chinese: 我這個星期三想去小明的家打球，可是那天看起來會下雨。 Pinyin: wǒ zhèi ge xīngqi sān xǐang qù Xǐaomíng de jiā dǎ qiú, kěshì nà tiān kàn qǐ lái huì xiàyǔ. Grammar structure: subj + date + verb + obj clause subj: 我 date: 这个星期三 verb: 想去 obj clause: 小明的家打球 connecting but: 可是 date: 那天 verb clause: 看起来会下雨

### Subject: Statistics

Given the stats below, what is the probability that a woman has cancer if she has a positive mammogram result? -1% of women over 50 have breast cancer -90% of women who have breast cancer test positive on mammograms -8% of women will have false positives

This is a classic example of Bayesian statistics. The equation takes the general form of: P(B|A) = P(B and A) / P(A) = P(B and A) / [P(B and A) + P(not B and A)] and we're solving for P(B|A). Using the laws of probability: P(B and A) = P(A|B)*P(B) P(not B and A) = P(A | not B) * P(not B) We can plug these in into the equation above later. In this example, A = positive test result B = has cancer P(B) = 0.01 (1% of women over 50 have breast cancer) P(not B) = 0.99 (99% of women over 50 do not have breast cancer) P(A|B) = 0.9 (Given the women that actually have breast cancer, 90% of those tested positive) P(A | not B) = 0.08 (Given the women that do not have breast cancer, 8% of those tested positive) Thus, we get P(B and A) = P(A|B)*P(B) = 0.9*0.01 P(not B and A) = P(A | not B) * P(not B) = 0.08*0.99 P(A) = P(B and A) + P(not B and A) = (0.9*0.01) + (0.08*0.99) P(B|A) = P(B and A) / P(A) = (0.9*0.01) / ((0.9*0.01) + (0.08*0.99)) = 0.1 The probability of a woman having cancer, given that she gets a positive test result, is 10%.

### Subject: Algebra

Find the equation of the line through the point (3, 0) and is perpendicular to the line through the points (2, 1) and (4, 5).

The general equation of a line takes the form y=mx+b. The first step to this question to is find the slope of (2, 1) and (4, 5). Then, find the perpendicular slope of those coordinates by taking the negative reciprocal. Once you have the perpendicular slope, that will be your 'm' in y=mx+b, and then you can find the equation that passes through (3, 0). Let's break it down. To find the slope of (2, 1) and (4, 5), you would use the equation (y2-y1)/(x2-x1). In this example, it would come out to be (5-1)/(4-2) = 2. Then find the slope of a line perpendicular to 2 by taking the negative reciprocal. For a slope of n, the negative reciprocal would be -1/n. In this case, the perpendicular slope would be -1/2. Thus, m = -1/2 or -0.5. Next, let's find the equation that passes through (3, 0). m = -0.5 from above. x=3 and y=0. All we have to do is plug those numbers into y=mx+b. 0 = -0.5 * 3 + b Solving for b, we get 3/2 or 1.5. Taking the m=-0.5 from above and b=1.5, our final equation would then be y=-0.5x+1.5 or in fraction form, y=(-1/2)x + 3/2.

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