Ray and lilli are designing their own shoes. they have 4 color options for the base and 6 color options for the accent. they can also pick 2 fonts for the embroidery. what is the probability that ray and lilli design identical shoes?

To solve this problem, let us first calculate the probability of designing one shoe out of all the combinations.

Probability of designing one shoe = (probability of choosing 1 color for the base) * (probability of choosing 1 color for the accent) * (probability of choosing 1 font for the embroidery)

We know that probability is:

Probability = number of chosen event / number of total events

Therefore:

Probability of designing one shoe = (1 / 4) * (1 / 6) * (1 / 2)

Probability of designing one shoe = 1 / 48

This means that either Ray or Lilli has this probability of designing a specific shoe. Since we are asked for the probability that they will both design this specific shoe, so we multiply:

Probability they will design the same shoe = (1 / 48) * (1 / 48)

Probability they will design the same shoe = 1 / 2304 = 4.34 * 10^-4

The probability is around 0.043% that they will design the same shoe.

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