Sleeping Beauty
Sleeping Beauty has an unusual neurological condition. When she wakes in the morning she cannot recall events of the past few days, and it takes an hour for her short-term memory to return.
One thing she does remember is that she is in the middle of an ongoing experiment. Every Sunday evening a fair coin is flipped and if it is heads, she is awakened Monday morning at 7, and if it is tails, she is awakened at 7 both Monday and Tuesday mornings. Otherwise (on all other mornings) she sleeps peacefully till 8.
One morning she is wakened at 7, and asked for the probability that the coin that was flipped the previous Sunday was heads. Just to be clear about her memory, at that moment, she knows that she has been awakened but she does not know whether it is Monday or Tuesday.
Since she studied probability with RabbitMath, she knows how to work this out. What answer does she give?
Sleeping Beauty Teacher Manual