There is a card-drawing prize activity with the following rules: In an opaque box, there are 2 cards marked with ``1000 yuan'' and 3 cards marked with ``0 yuan''. A participant randomly draws one card from the box. Without knowing the amount marked on the drawn card, the host then places a card marked with ``500 yuan'' into the box. At this point, the participant has two choices: (I) Keep the originally drawn card; the amount marked on that card is the prize won. (II) Discard the originally drawn card without returning it, and randomly draw another card from the box; the amount marked on that card is the prize won. A participant joins this activity. Assume each card has an equal chance of being drawn. Select the correct options. (1) If the participant chooses (I), the probability of winning 0 yuan is $\frac { 3 } { 5 }$ (2) If the participant chooses (I), the expected value of the prize is 500 yuan (3) If the participant chooses (II), the probability of winning 1000 yuan is $\frac { 2 } { 5 }$ (4) If the participant chooses (II), the probability of winning 0 yuan is $\frac { 12 } { 25 }$ (5) If the participant chooses (II), the expected value of the prize is 420 yuan
There is a card-drawing prize activity with the following rules:\\
In an opaque box, there are 2 cards marked with ``1000 yuan'' and 3 cards marked with ``0 yuan''. A participant randomly draws one card from the box. Without knowing the amount marked on the drawn card, the host then places a card marked with ``500 yuan'' into the box. At this point, the participant has two choices:\\
(I) Keep the originally drawn card; the amount marked on that card is the prize won.\\
(II) Discard the originally drawn card without returning it, and randomly draw another card from the box; the amount marked on that card is the prize won.
A participant joins this activity. Assume each card has an equal chance of being drawn. Select the correct options.\\
(1) If the participant chooses (I), the probability of winning 0 yuan is $\frac { 3 } { 5 }$\\
(2) If the participant chooses (I), the expected value of the prize is 500 yuan\\
(3) If the participant chooses (II), the probability of winning 1000 yuan is $\frac { 2 } { 5 }$\\
(4) If the participant chooses (II), the probability of winning 0 yuan is $\frac { 12 } { 25 }$\\
(5) If the participant chooses (II), the expected value of the prize is 420 yuan