please share all your thoughts about this.

In a game show, Sana, Nayeon, and Dahyun played as prisoners where they played mini games for them to be released. The top two winners of the mini games will be released, and the 3rd placer will be declared as loser. However, the three players have equal scores in the mini games. The game show crew will now decide which two of the three prisoners will be released, and the three players know this but not which two. One of the crew is a friend of Sana, and the crew knows who are to be released. Sana realizes that it would be unethical to ask the crew if she is to be released but thinks of asking for the name of one player other than herself who is to be released. She thinks that before she asks, her chances of release are 2/3. She thinks that if the crew says \"Nayeon will be released,\" her own chances have gone down to 1/2, because either Sana and Nayeon or Dahyun and Nayeon are to be released. And so, Sana decides not to reduce her chances by asking. For simplicity, let A = Sana, B = Nayeon, and C = Dahyun. A. The table gives the sample space of the experiment, nd the corresponding probabilities of each outcome in the sample space: Probability A and B will be released, the crew says B A and C will be released, the crew says C B and C will be released. B and C will be released, the crew says B B and C will be released, the crew says C B. Based on item A, Sana is mistaken in her calculations. Explain. Without asking the crew, Sana's probability of release is If she asks the crew and the crew says, "Nayeon will be released," her probability of release will be This is the (write either same or opposite, small caps) of what she is thinking, oilitWithout asking the crew, Sana's probability of release is . If she asks the crew and the crew says, \"Nayeon will be released,\" her probability of release will be . This is the I (write either same or opposite, small caps) of what she is thinking, that is, her probability of release will actually | I (write either increase or decrease, small caps) if she will ask the crew