Question

Selecting two marbles from a bag containing the numbers 2,4,6,8,10,12 (with replacement) what is the probability of selecting two numbers less than 10 ?

Answer 1

Given:

A bag containing the numbers 2,4,6,8,10,12.

To find:

The probability of selecting two numbers less than 10.

Solution:

We have,

Total numbers = 6

Numbers less than 10 are 2,4,6,8.

Numbers less than 10 = 4

Probability of getting a number less than 10 is:

$P(\text{Less than 10})=\dfrac{\text{Numbers less than 10}}{\text{Total numbers}}$

$P(\text{Less than 10})=\dfrac{4}{6}$

$P(\text{Less than 10})=\dfrac{2}{3}$

We select the second number with replacement. So, the probability of second draw is same as the probability for first draw.

Probability of selecting two numbers less than 10 is:

$\text{Required probability}=P(\text{Less than 10})\times P(\text{Less than 10})$

$\text{Required probability}=\dfrac{2}{3}\times \dfrac{2}{3}$

$\text{Required probability}=\dfrac{4}{9}$

Therefore, the probability of selecting two numbers less than 10 is $\dfrac{4}{9}$.