Question

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? 1/24, 1/8, 1/4 or 1/3

Answer 1

Answer :-Probability that the sequence is guessed on the first try

$=\frac{1}{24}$

Explanation :-

Total colors available for making code= 4

Color required for making code =3

As once one color is used, it cannot be repeated in the sequence.

then by using permutation the total ways of making code = $A=^4P_3=\frac{4!}{(4-3)!}\\=\frac{4\times3\times2\times1}{1!}=24$

Now probability that the sequence is guessed on the first try

$\frac{1}{\text{total ways of making code}}=\frac{1}{24}$

Answer 2

Answer:

1/24

Step-by-step explanation:

we are given that:

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.

We have to find the probability that the sequence is guessed on the first try.

Total ways of making a code=$4_{P_{3} } =\dfrac{factorial4}{factorial1}$

                                               =24

Now, we have to guess in the first try

So, P(The sequence is guessed on the first try)=1/24