Question

To make a $750$-piece jigsaw puzzle more challenging, a puzzle company includes $5$ extra pieces in the box along with the $750$ pieces, and those $5$ extra pieces do not fit anywhere in the puzzle. If you buy such a puzzle box, break the seal on the box, and immediately select 1 piece at random, what is the probability that it will be 1 of the extra pieces?

• A. $\frac{1}{5}$
• B. $\frac{1}{755}$
• C. $\frac{1}{750}$
• D. $\frac{5}{755}$
• E. $\frac{5}{750}$

Answer 1

The correct option is D $\frac{5}{755}$

Total number of pieces in the puzzle $750+5\text{extra pieces}=755$ pieces.

Therefore, the number of ways of selecting $1$ piece at random is $755C_1$

$\Rightarrow n\left(S\right)=755$

Total number of extra pieces is $5$.

Let $A$ be the event of selecting $1$ piece of the extra pieces.

Therefore, number of ways of selecting $1$ piece of the extra pieces is $5C_1$.

$\Rightarrow n\left(A\right)=5$

Therefore, the probability that it will be 1 of the extra pieces is $P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$

$\Rightarrow P\left(A\right)=\frac{5}{755}$

Hence, the probability that it will be 1 of the extra pieces is $\frac{5}{755}$.