# The probability of obtaining an even prime number on each die, when a pair of dice is rolled

is:

(a) 0

(b) \[\dfrac{1}{3}\]

(c) \[\dfrac{1}{12}\]

(d) \[\dfrac{1}{36}\]

Last updated date: 21st Mar 2023

•

Total views: 306.6k

•

Views today: 7.85k

Answer

Verified

306.6k+ 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

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE