A die is rolled. Find the probability of the given event.
(a) The number showing is a 5;
The probability is?
(b) The number showing is an even number;
The probability is ?
(c) The number showing is greater than 5;
The probability is?
well, there are 6 possible events.
How many for success in each question?
Is letter c a 3?
first off, any probability is at most 1.
(c)
There is only one number on a die which is greater than 5.
So, of the 6 events, only 1 is a success.
So, p(x>5) = 1/6
Ok, what is b?
To find the probability of an event, you need to divide the number of favorable outcomes by the total number of possible outcomes.
In this case, we have a fair six-sided die, so the total number of possible outcomes is 6.
(a) The number showing is a 5:
There is only one favorable outcome (rolling a 5) out of the six possible outcomes.
So, the probability is 1/6.
(b) The number showing is an even number:
There are three favorable outcomes (rolling a 2, 4, or 6) out of the six possible outcomes.
So, the probability is 3/6, which simplifies to 1/2.
(c) The number showing is greater than 5:
There is one favorable outcome (rolling a 6) out of the six possible outcomes.
So, the probability is 1/6.
Keep in mind that probabilities are always between 0 and 1, inclusive.