Answer
Verified
480.3k+ views
Hint: We know that 2 is an only even prime number, so first we have to find the probability of getting 2 on each die and then multiply them to get the required value of probability.
Here, we are given that a pair of dice is rolled. We have to find the probability of obtaining an even prime number on each die.
First of all, we know that there is just one even prime number and that is 2. All other prime numbers except 2 are odd.
Therefore, here we have to find the probability of getting 2 on each die.
We know that a die has a total of 6 faces and each face has different numbers that are 1, 2, 3, 4, 5, and 6.
Now, when we roll a die we can get any one of these 6 numbers.
Therefore, the total outcomes of rolling a die = 6.
Now, out of 6 outcomes, there would be just 1 outcome when we would get the number 2 on the die.
Therefore, the probability of obtaining the number 2 when a die is rolled is:
\[\begin{align}
& =\dfrac{\text{No}\text{.of Favorable Outcomes}}{\text{No}\text{.of total outcomes}} \\
& =\dfrac{1}{6} \\
\end{align}\]
Now, when the other die is rolled, the probability of getting 2 would again be \[\dfrac{1}{6}\].
Therefore, when this pair of dice is rolled, the probability of obtaining 2 on each die is
\[=\left( \text{Probability of getting 2 on one die} \right)\times \left( \text{Probability of getting 2 on the other die} \right)\]
\[=\dfrac{1}{6}\times \dfrac{1}{6}\]
\[=\dfrac{1}{36}\]
Hence, option (d) is correct.
Note: This question can also be solved as follows:
When two dice are rolled, the total number of outcomes are
\[6\times 6=36\]
Now, we know that there would be just 1 out of 36 outcomes when we would get 2 on both dice.
Therefore, the probability of getting 2 on each die
\[\begin{align}
& =\dfrac{\text{No}\text{.of Favorable Outcomes}}{\text{No}\text{.of total outcomes}} \\
& =\dfrac{1}{36} \\
\end{align}\]
which is the required value.
Here, we are given that a pair of dice is rolled. We have to find the probability of obtaining an even prime number on each die.
First of all, we know that there is just one even prime number and that is 2. All other prime numbers except 2 are odd.
Therefore, here we have to find the probability of getting 2 on each die.
We know that a die has a total of 6 faces and each face has different numbers that are 1, 2, 3, 4, 5, and 6.
Now, when we roll a die we can get any one of these 6 numbers.
Therefore, the total outcomes of rolling a die = 6.
Now, out of 6 outcomes, there would be just 1 outcome when we would get the number 2 on the die.
Therefore, the probability of obtaining the number 2 when a die is rolled is:
\[\begin{align}
& =\dfrac{\text{No}\text{.of Favorable Outcomes}}{\text{No}\text{.of total outcomes}} \\
& =\dfrac{1}{6} \\
\end{align}\]
Now, when the other die is rolled, the probability of getting 2 would again be \[\dfrac{1}{6}\].
Therefore, when this pair of dice is rolled, the probability of obtaining 2 on each die is
\[=\left( \text{Probability of getting 2 on one die} \right)\times \left( \text{Probability of getting 2 on the other die} \right)\]
\[=\dfrac{1}{6}\times \dfrac{1}{6}\]
\[=\dfrac{1}{36}\]
Hence, option (d) is correct.
Note: This question can also be solved as follows:
When two dice are rolled, the total number of outcomes are
\[6\times 6=36\]
Now, we know that there would be just 1 out of 36 outcomes when we would get 2 on both dice.
Therefore, the probability of getting 2 on each die
\[\begin{align}
& =\dfrac{\text{No}\text{.of Favorable Outcomes}}{\text{No}\text{.of total outcomes}} \\
& =\dfrac{1}{36} \\
\end{align}\]
which is the required value.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE