A die is rolled. Find the probability of the given event.
(a) The number showing is a 6;
(b)The number showing is an even number;
The probability is;
(c) The number showing is greater than 2;
The probability is
We'll be glad to check your answers.
(A) 6 is 1 out of 6 probabilities.
(B) How many even numbers are there from 1-6?
(C) How many numbers of a die are greater than 2?
1/2
To find the probability of an event, we need to determine the number of favorable outcomes (the event we're interested in) and divide it by the total number of possible outcomes.
(a) The number showing is a 6:
There is one favorable outcome (rolling a 6) and six equally likely possible outcomes (rolling a number from 1 to 6). Therefore, the probability of rolling a 6 is 1/6.
(b) The number showing is an even number:
Out of the six possible outcomes, there are three even numbers (2, 4, and 6) and three odd numbers (1, 3, and 5). So, the probability of rolling an even number is 3/6, which simplifies to 1/2.
(c) The number showing is greater than 2:
Out of the six possible outcomes, there are four numbers greater than 2 (3, 4, 5, and 6) and two numbers that are not (1 and 2). Therefore, the probability of rolling a number greater than 2 is 4/6, which simplifies to 2/3.