Which of the following experiments have equally likely outcomes? Explain.
A driver attempts to start a car. The car starts or does not start.
Not equally likely
Tossing a fair coin once.
Equally likely
Rolling a fair 6-sided die.
Equally likely
Choosing a marble randomly from a bag that contains 3 red marbles and 7 blue marbles.
Not equally likely
A baby is born. It is a boy or a girl.
Equally likely
Explanation
Outcomes are considered equally likely when there is no reason to believe that any one outcome is more likely than another.
(i) A driver attempts to start a car: The outcomes (car starts or does not start) are not equally likely. The probability depends heavily on the condition of the car, making one outcome more probable than the other.
(ii) Tossing a fair coin once: The outcomes (Heads or Tails) are equally likely. Because the coin is fair, there is no reason to believe one side is more likely to appear than the other.
(iii) Rolling a fair 6-sided die: The outcomes (1, 2, 3, 4, 5, or 6) are equally likely. A fair die ensures that each number has the exact same chance of appearing.
(iv) Choosing a marble randomly from a bag with 3 red and 7 blue marbles: The outcomes are not equally likely. Since there are different quantities of marbles (7 blue vs 3 red), drawing a blue marble is more likely than drawing a red one.
(v) A baby is born: The outcomes (boy or girl) are equally likely. There is no reason to believe that the birth of a boy is more likely than the birth of a girl, or vice versa.