Compute the probability of tossing a six-sided die and getting a number less than 3.
Answer (2)
Identify favorable outcomes: rolling a 1 or 2.
Count favorable outcomes: there are 2.
Calculate the probability: 6 2 .
Simplify the fraction: 3 1 .
Explanation
Analyze the problem When tossing a six-sided die, the possible outcomes are the numbers 1, 2, 3, 4, 5, and 6. We want to find the probability of getting a number less than 3.
Identify favorable outcomes The numbers less than 3 are 1 and 2. So, there are 2 favorable outcomes. The total number of possible outcomes is 6.
Calculate the probability The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the probability of getting a number less than 3 is: P ( n u mb er < 3 ) = t o t a l u mb ero f o u t co m es n u mb ero ff a v or ab l eo u t co m es = 6 2
Simplify the fraction We can simplify the fraction 6 2 by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 6 2 = 6 ÷ 2 2 ÷ 2 = 3 1
State the final answer The probability of tossing a six-sided die and getting a number less than 3 is 3 1 .
Examples
Imagine you're playing a board game where you need to roll a number less than 3 to move forward. Knowing this probability helps you understand your chances of advancing on any given turn. For example, if you need to roll less than 3 to land on a special spot, you know you have a 1/3 chance each time you roll the die. This kind of probability is also useful in games of chance, like predicting outcomes in simple bets or understanding the odds in a lottery.
The probability of getting a number less than 3 when tossing a six-sided die is 3 1 . This is calculated by identifying the favorable outcomes (1 and 2) and dividing by the total possible outcomes (6). After simplifying, the answer remains 3 1 .
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