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A child's game has $8$ triangles of which $3$ are blue and rest are red and $10$ squares of which $6$ are blue and rest are red. One piece is lost at random. Find the probability that it is a square.

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\frac{1}{9}

\frac{5}{10}

\frac{4}{9}

\frac{5}{9}

answer is D.

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Detailed Solution

Given that a child's game has

8

triangles of which

3

are blue and rest are red and

10

squares of which

6

are blue and rest are red. One piece is lost at random.
We are given to find the probability that it is a square.
For an event E, probability is given by,

P E = Number of favourable outcomes n(E) Total number of outcomes n(S)

Total number of articles,

n S = 10 + 8 ⇒ n S = 18

The total number of squares is 10.
So, n(E) = 10.
The probability that lost piece is a square is calculated as follows:

P E = 1018 ⇒ P E = 59

Thus, the probability that lost piece is a square is

59

.
Hence, the correct option is 4.

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