MATH 1550H Quiz: MATH1550H-Quiz-Solutions (1)
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[2: draw the complete tree diagram for this experiment. The sample space is = { (h, 1), (h, 2), (h, 3), (t, 2), (t, 3), (t, 4) }. The probability mass function turns out to be uniform: for each outcome we toss the fair coin, with p (h) = p (t ) = 1. 2 , and then roll a fair three-sided die, with each face having a probability of 1. 3 , so each outcome has probability m( ) = 1. 3 = 1 m(h, 1) = m(h, 2), = m(h, 3) = m(t, 2) = m(t, 3) = m(t, 4) = 2. (cid:3: there are two outcomes that have a 2 as the face that occurred in the roll of the die, namely (h, 2) and (t, 2). Thus the probability of this event, call it a, is. P (a) = m(h, 2) + m(t, 2) =
