Question

Suppose we have two weighted coins, one of which comes up heads with probability 0.2, and the other of which comes up heads with probability 0.6. unfortunately, the coins are otherwise identical, and we have lost track of which is which. suppose we flip a randomly chosen coin 12 times and let n be the random variable giving the number of heads seen. if in the first 3 flips we see 2 heads, what is the conditional expected number of heads in the 12 flips?

Answer 1

the expected number of heads seen in 12 flips is 8 heads seen

Answer 2

The expected number of a dataset is the mean of the dataset.

The expected number of heads in 12 flips is 10

The given parameters are:

$\mathbf{n = 12}$

$\mathbf{p_1 = 0.2}$

$\mathbf{p_2 = 0.6}$

The expected number (E) is calculated using:

$\mathbf{E = np}$

So, we have:

$\mathbf{E = n(p_1 + p_2)}$

This gives

$\mathbf{E = 12 \times (0.2 + 0.6)}$

$\mathbf{E = 12 \times 0.8}$

$\mathbf{E = 9.6}$

Approximate

$\mathbf{E = 10}$

Hence, the expected number of heads in 12 flips is 10

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