Class 12 Exam > Class 12 Videos > Example: Rolling even three times - Probability, Mathematics
Example: Rolling even three times - Probability, Mathematics Video Lecture - Class 12
FAQs on Example: Rolling even three times - Probability, Mathematics Video Lecture - Class 12
| 1. What is the probability of rolling an even number three times in a row? |  |
Ans. To calculate the probability of rolling an even number three times in a row, we need to consider the total number of outcomes and the favorable outcomes.
The total number of outcomes when rolling a fair six-sided die three times is 6 * 6 * 6 = 216.
Now, let's determine the number of favorable outcomes. The probability of rolling an even number on a single roll is 3/6 (as there are three even numbers - 2, 4, and 6 - out of a total of six numbers).
Since we are rolling three times in a row, the probability of rolling an even number on each roll is (3/6) * (3/6) * (3/6) = 1/8.
Therefore, the probability of rolling an even number three times in a row is 1/216.
| 2. What is the probability of rolling an odd number at least once in three rolls? | |
Ans. To find the probability of rolling an odd number at least once in three rolls, we can use the principle of complementary probability.
The probability of not rolling an odd number on a single roll is 3/6 (as there are three odd numbers - 1, 3, and 5 - out of a total of six numbers).
Since we are rolling three times in a row, the probability of not rolling an odd number on any of the rolls is (3/6) * (3/6) * (3/6) = 1/8.
To find the probability of rolling an odd number at least once, we subtract this probability from 1 (since the sum of the probabilities of all possible outcomes is 1).
Therefore, the probability of rolling an odd number at least once in three rolls is 1 - 1/8 = 7/8.
| 3. If I roll a fair six-sided die three times, what is the probability of getting the same number on each roll? | |
Ans. To calculate the probability of getting the same number on each roll when rolling a fair six-sided die three times, we need to determine the number of favorable outcomes.
Since there are six possible outcomes on each roll, the number of favorable outcomes is 6 (as there are six numbers to choose from).
The total number of outcomes when rolling a die three times is 6 * 6 * 6 = 216.
Therefore, the probability of getting the same number on each roll is 6/216, which simplifies to 1/36.
| 4. Is it more likely to roll an even number three times in a row or to roll an odd number at least once in three rolls? | |
Ans. To compare the likelihood of rolling an even number three times in a row and rolling an odd number at least once in three rolls, we can compare their probabilities.
The probability of rolling an even number three times in a row is 1/216, as calculated earlier.
On the other hand, the probability of rolling an odd number at least once in three rolls is 7/8, also calculated earlier.
Comparing these probabilities, we can conclude that it is more likely to roll an odd number at least once in three rolls (7/8) than to roll an even number three times in a row (1/216).
| 5. What is the probability of rolling an even number on the first two rolls and an odd number on the third roll? | |
Ans. To calculate the probability of rolling an even number on the first two rolls and an odd number on the third roll, we multiply the individual probabilities of each roll.
The probability of rolling an even number on a single roll is 3/6 (as there are three even numbers - 2, 4, and 6 - out of a total of six numbers).
Since we are rolling three times in a row, the probability of rolling an even number on the first two rolls is (3/6) * (3/6) = 1/4.
Similarly, the probability of rolling an odd number on the third roll is 3/6.
Therefore, the probability of rolling an even number on the first two rolls and an odd number on the third roll is (1/4) * (3/6) = 1/8.
Text Transcript from Video
Find the probability of rolling
even numbers three
times using a six-sided die
numbered from 1 to 6.
So let's just figure out the
probability of rolling it each
of the times.
So the probability of rolling
even numbers.
So even roll on six-sided die.
So let's think about
that probability.
Well, how many total
outcomes are there?
How many possible rolls
could we get?
Well, you get one, two, three,
four, five, six.
And how many of them satisfy
these conditions, that it's an
even number?
Well, it could be a 2,
it could be a 4, or
it could be a 6.
So the probability is the events
that match what you
need, your condition for right
here, so three of the possible
events are an even roll.
And it's out of a total of
six possible events.
So there is a-- 3 over 6 is
the same thing as 1/2
probability of rolling
even on each roll.
Now they're going to
roll-- they want to
roll even three times.
And these are all going to
be independent events.
Every time you roll, it's not
going to affect what happens
in the next roll, despite what
some gamblers might think.
It has no impact on what happens
on the next roll.
So the probability of rolling
even three times is equal to
the probability of an even roll
one time, or even roll on
six-sided die-- this thing over
here is equal to that
thing times that thing again.
All right, that's our first
roll-- we copy and we paste
it-- times that thing and then
times that thing again.
Right?
That's our first roll,
which is that.
That's our second roll.
That's our third roll.
They're independent events.
So this is going to be equal to
1/2-- that's the same 1/2
right there-- times 1/2
times 1/2, which is
equal to 1 over 8.
There's a 1 in 8 possibility
that you roll even numbers on
all three rolls.
On this roll, this roll,
and that roll.
even numbers three
times using a six-sided die
numbered from 1 to 6.
So let's just figure out the
probability of rolling it each
of the times.
So the probability of rolling
even numbers.
So even roll on six-sided die.
So let's think about
that probability.
Well, how many total
outcomes are there?
How many possible rolls
could we get?
Well, you get one, two, three,
four, five, six.
And how many of them satisfy
these conditions, that it's an
even number?
Well, it could be a 2,
it could be a 4, or
it could be a 6.
So the probability is the events
that match what you
need, your condition for right
here, so three of the possible
events are an even roll.
And it's out of a total of
six possible events.
So there is a-- 3 over 6 is
the same thing as 1/2
probability of rolling
even on each roll.
Now they're going to
roll-- they want to
roll even three times.
And these are all going to
be independent events.
Every time you roll, it's not
going to affect what happens
in the next roll, despite what
some gamblers might think.
It has no impact on what happens
on the next roll.
So the probability of rolling
even three times is equal to
the probability of an even roll
one time, or even roll on
six-sided die-- this thing over
here is equal to that
thing times that thing again.
All right, that's our first
roll-- we copy and we paste
it-- times that thing and then
times that thing again.
Right?
That's our first roll,
which is that.
That's our second roll.
That's our third roll.
They're independent events.
So this is going to be equal to
1/2-- that's the same 1/2
right there-- times 1/2
times 1/2, which is
equal to 1 over 8.
There's a 1 in 8 possibility
that you roll even numbers on
all three rolls.
On this roll, this roll,
and that roll.
About this Video
Oct 12, 2025
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