Question

lydia runs an experiment to determine if a coin is fair by counting the number of times a coin lands heads up. the table shows her data.
coin fairness test

number of coin flips	0	10	20	30	40	50	60	70	80	90
number of heads up	0	7	12	18	23	30	35	38	42	45

according to the line of best fit, about how many times would the coin land heads up in 100 flips?
48
50
51
53

Explanation:

Step1: Calculate the proportion of heads - up

We first find the proportion of heads - up for the given data points. For example, when the number of coin flips is \(n = 10\), the number of heads - up is \(h=7\), and the proportion \(p_1=\frac{7}{10} = 0.7\); when \(n = 20\), \(h = 12\), and \(p_2=\frac{12}{20}=0.6\); when \(n = 30\), \(h = 18\), and \(p_3=\frac{18}{30}=0.6\); when \(n = 40\), \(h = 23\), and \(p_4=\frac{23}{40}=0.575\); when \(n = 50\), \(h = 30\), and \(p_5=\frac{30}{50}=0.6\); when \(n = 60\), \(h = 35\), and \(p_6=\frac{35}{60}\approx0.583\); when \(n = 70\), \(h = 38\), and \(p_7=\frac{38}{70}\approx0.543\); when \(n = 80\), \(h = 42\), and \(p_8=\frac{42}{80}=0.525\); when \(n = 90\), \(h = 45\), and \(p_9=\frac{45}{90}=0.5\).

Step2: Predict for 100 flips

As the number of flips increases, the proportion seems to be approaching \(0.5\). If we assume a linear - like trend (since we are talking about the line of best fit), for a fair coin, the theoretical probability of getting heads is \(0.5\). For \(n = 100\) flips, the expected number of heads - up is \(E=0.5\times100 = 50\).

Answer:

50