Question

A game has 8 triangles of which 6 are blue and rest are green, 12 rectangles of which 3 are green and rest are blue, and 10 rhombuses of which 3 are blue rest are green. One piece is lost at random. Find the probability that it is a green triangle.

Answer 1

Hint: In this question, we are going to find out the probability of a green triangle that is lost. First, we will check how many possible outcomes there are, that is we will check how many objects are there. After that, we will check how many triangles, rectangles and rhombuses are there of green and blue colour. We are going to use the formula which is from the probability topic. The formula is a total number of favorable events (E) divided by a total number of possible outcomes(S).

Complete step by step answer:
We have given in the question that there are 8 triangles, 10 rhombuses and 12 rectangles.
In 8 triangles, we have 6 of blue colour and 2 of green colour.
In 12 rectangles, we have 3 of green colour and 9 of blue colour.
In 10 rhombuses, we have 3 of blue colour and 7 of green colour.
Total sum of all the outcomes n(S) = 8+12+10=30
Now, for finding the probability that the loss is a green triangle (as there are green 2 triangles)
As, \[n(E)=2\]
\[P(E)=\dfrac{n(E)}{n(S)}\]
\[\Rightarrow \]\[P(E)=\dfrac{2}{30}\]
Therefore, the outcome is
\[P(E)=\dfrac{1}{15}\].

Note:
 One should have proper knowledge in probability. In this type of question, we can find the value or the probability by the formula: Number of green triangles that can be lost/Total number of objects. This will be a simple formula for finding the solution of these types of questions.