We model the experiment where we toss a fair coin 4 times as follows. The sample...

We model the experiment where we toss a fair coin 4 times as follows. The sample space Ω is the space of (ordered) binary vectors of length 4. A 1 in the i-th position of such a binary vector indicates Heads at the i-th toss. The probability measure (P) on Ω is defined as P(A)=|A| / |Ω| for all A⊂Ω. Let Ai be the event that the ith toss is Heads, i = 1,...,4. (a) Give all outcomes in A3. (b) Show that, with the above probability measure P, the events A1, . . . , A4 are mutually independent. (c) Give P(A1 ∩ A2 | A1) and P(A1 ∪ A3 | A2)

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orchestra answered 1 year ago

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