QUESTION 3
Easy
Which of the following experiments have equally likely outcomes? Explain.
(i) A driver attempts to start a car. The car starts or does not start.
(ii) Tossing a fair coin once.
(iii) Rolling a fair 6-sided die.
(iv) Choosing a marble from a bag that contains 3 red marbles and 7 blue marbles.
(v) A baby is born. It is a boy or a girl.
SOLUTION
1
(i) A driver attempts to start a car
Possible outcomes:
(i) car starts
(ii) car does not start
These outcomes are not equally likely because a car is usually more likely to start than fail.
(i) car starts
(ii) car does not start
These outcomes are not equally likely because a car is usually more likely to start than fail.
2
(ii) Tossing a fair coin once
Possible outcomes:
(i) Head(H)
(ii) Tail(T)
For a fair coin, \(P(H) = P(T)= \frac{1}{2}\)
Both outcomes have the same chance so they are equally likely to occur.
(i) Head(H)
(ii) Tail(T)
For a fair coin, \(P(H) = P(T)= \frac{1}{2}\)
Both outcomes have the same chance so they are equally likely to occur.
3
(iii) Rolling a fair 6-sided die
Possible outcomes: \(1, 2, 3, 4, 5, 6\)
For a fair die, each number has probability = \(\frac{1}{6}\)
So all outcomes are equally likely.
For a fair die, each number has probability = \(\frac{1}{6}\)
So all outcomes are equally likely.
4
(iv) Choosing a marble from a bag that contains 3 red and 7 blue marbles
Possible outcomes:
(i) Red marble
(ii) Blue marble
Probabilities:
\(P(Red) = \frac{3}{10}\)
\(P(Blue) = \frac{7}{10}\)
Since the probabilities are different, the outcomes are not equally likely.
(i) Red marble
(ii) Blue marble
Probabilities:
\(P(Red) = \frac{3}{10}\)
\(P(Blue) = \frac{7}{10}\)
Since the probabilities are different, the outcomes are not equally likely.
5
(v) A baby born is a boy or a girl
Possible outcomes:
(i) Boy
(ii) Girl
\(P(Boy) = P(Girl)\)
So the outcomes are equally likely.
(i) Boy
(ii) Girl
\(P(Boy) = P(Girl)\)
So the outcomes are equally likely.
🏆
Final Answer :
(i) Not equally likely
(ii) Equally likely
(iii) Equally likely
(iv) Not equally likely
(v) Equally likely
Concept Note
Two or more outcomes are equally likely if each outcome has the same probability.
If one outcome has a greater chance than another, the outcomes are not equally likely.