Once a customer fills the car with gas at one station, that customer cannot then go fill the same car with gas at another station right away. Are the outcomes E1, E2, E3, and E4 mutually exclusive? Explain.

Yes, the outcomes E1, E2, E3, and E4, which represent filling a car with gas at different gas stations, are mutually exclusive. By definition, mutually exclusive events are those events that cannot occur at the same time. In other words, if one event happens, the other cannot happen in the same context.

When a customer fills their car's tank at one gas station (say event E1 happens), the tank reaches its capacity, and they cannot go immediately to another station to fill the tank again. This is because the tank can only hold a limited amount of gas, and once full, there is no room for more until some of the gas has been used. Therefore, if a customer fills up their car at station 1 (E1), they physically cannot fill up at station 2 (E2), station 3 (E3), or station 4 (E4) right after that, making events E1, E2, E3, and E4 mutually exclusive.