Then by your logic, you ought to say that your probability of waking in the morning is (1/4)x(0/2) + (1/2)x(6/7) + (1/4)x(12/12) = 3⁄7 + 1⁄4 = 19⁄28, rather than 1⁄2 if the coins are tossed ‘just in time’.
By neq1′s previous reasoning, there’s 50% chance of waking in the mornings and 50% chance of waking in the evening for any particular week. That is the case whether the coins are tossed in advance or not. The probability of a particular morning awakening would be 1⁄12.
I’m not sure where you got your (6/7) figure for neq1′s calculations.
I’m not sure where you got your (6/7) figure for neq1′s calculations.
neq1 admits that in my original scenario, before I introduced the coin and hibernations, you have a 6⁄7 probability of waking in the morning. The case where one of the two coins is heads and the other is tails is equivalent to this.
By neq1′s previous reasoning, there’s 50% chance of waking in the mornings and 50% chance of waking in the evening for any particular week. That is the case whether the coins are tossed in advance or not. The probability of a particular morning awakening would be 1⁄12.
I’m not sure where you got your (6/7) figure for neq1′s calculations.
neq1 admits that in my original scenario, before I introduced the coin and hibernations, you have a 6⁄7 probability of waking in the morning. The case where one of the two coins is heads and the other is tails is equivalent to this.