Question

how many heads would you expect if you flipped a coin twice?
first, fill in the table with the correct probabilities.
hint: the sample space for flipping a coin twice is hh, ht, th, tt.

the expected value for the number of heads is

the expected value in this case means

Explanation:

Step1: Calculate probability for 0 heads

The outcome with 0 heads is TT. There are 4 total outcomes in the sample space {HH, HT, TH, TT}. So the probability \( A=\frac{1}{4} \).

Step2: Calculate probability for 1 head

The outcomes with 1 head are HT and TH. So the number of favorable outcomes is 2. The probability \( B = \frac{2}{4}=\frac{1}{2} \).

Step3: Calculate probability for 2 heads

The outcome with 2 heads is HH. So the probability \( C=\frac{1}{4} \).

Step4: Calculate expected value

The formula for expected value \( E(X)=\sum_{i}x_ip_i \). Here \( x_1 = 0\), \(p_1=\frac{1}{4}\); \(x_2 = 1\), \(p_2=\frac{1}{2}\); \(x_3=2\), \(p_3=\frac{1}{4}\).

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Answer:

\( A=\frac{1}{4}\), \(B = \frac{1}{2}\), \(C=\frac{1}{4}\), expected value \(= 1\). The expected value in this case means that if we flip a coin twice many times, on average, we would get 1 head per two - coin - flip trial.