Answer :
To determine the probability that Betty will guess correctly on the fourth question of her test, we need to consider the nature of a multiple choice test. Each question on the test has 3 possible answers, one of which is correct.
1. Independent Events: The first step is to understand that each question on the test is an independent event. The outcome of one question does not affect the outcome of another. This means that whether Betty guesses correctly or incorrectly on the first three questions has no impact on her probability of guessing correctly on the fourth question.
2. Possible Outcomes: For each question, there are 3 possible answers, only one of which is correct.
3. Probability Calculation:
- The probability of choosing the correct answer from the 3 options for any single question is given by the ratio of the number of correct answers to the total number of possible answers.
- Since there is 1 correct answer and 3 possible answers, the probability [tex]\( P \)[/tex] of guessing correctly on any given question is given by:
[tex]\[ P = \frac{\text{Number of correct answers}}{\text{Total number of answers}} = \frac{1}{3} \][/tex]
Thus, the probability that Betty will guess correctly on the fourth question, given that each question is independent and has the same number of choices, is:
[tex]\[ \boxed{\frac{1}{3}} \][/tex]
1. Independent Events: The first step is to understand that each question on the test is an independent event. The outcome of one question does not affect the outcome of another. This means that whether Betty guesses correctly or incorrectly on the first three questions has no impact on her probability of guessing correctly on the fourth question.
2. Possible Outcomes: For each question, there are 3 possible answers, only one of which is correct.
3. Probability Calculation:
- The probability of choosing the correct answer from the 3 options for any single question is given by the ratio of the number of correct answers to the total number of possible answers.
- Since there is 1 correct answer and 3 possible answers, the probability [tex]\( P \)[/tex] of guessing correctly on any given question is given by:
[tex]\[ P = \frac{\text{Number of correct answers}}{\text{Total number of answers}} = \frac{1}{3} \][/tex]
Thus, the probability that Betty will guess correctly on the fourth question, given that each question is independent and has the same number of choices, is:
[tex]\[ \boxed{\frac{1}{3}} \][/tex]
