two children are playing a code - breaking game. one child makes a sequence of three colors from red…

two children are playing a code - breaking game. one child makes a sequence of three colors from red, yellow, blue, and purple. the other child must guess the sequence of colors in the correct order. once one color is used, it cannot be repeated in the sequence. what is the probability that the sequence is guessed on the first try? $\frac{1}{24}$ $\frac{1}{8}$ $\frac{1}{4}$ $\frac{1}{3}$

two children are playing a code - breaking game. one child makes a sequence of three colors from red, yellow, blue, and purple. the other child must guess the sequence of colors in the correct order. once one color is used, it cannot be repeated in the sequence. what is the probability that the sequence is guessed on the first try? $\frac{1}{24}$ $\frac{1}{8}$ $\frac{1}{4}$ $\frac{1}{3}$

Answer

Explanation:

Step1: Calculate total number of possible sequences

The number of permutations of 4 colors taken 3 at a time is given by the permutation formula $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 4$ and $r=3$. So $P(4,3)=\frac{4!}{(4 - 3)!}=\frac{4!}{1!}=4\times3\times2=24$.

Step2: Determine probability of guessing correctly on first try

There is only 1 correct sequence. The probability $P$ of guessing the correct sequence on the first try is the number of favorable outcomes (1) divided by the number of total outcomes (24). So $P=\frac{1}{24}$.

Answer:

$\frac{1}{24}$