15 plants are treated with the plant protection product and then sprayed with fungal spores. Determine the probability of each of the following events:\n$E _ { 1 }$ : ``None of the plants become infested with fungi.''\n$E _ { 2 }$ : ``At most two plants become infested with fungi.''\n$E _ { 3 }$ : ``12 or 13 plants remain free of fungal infestation.''