Question

a six sided cube with the letters s,o,l,v,e,d is rolled twice. what is the probability of rolling two consonants? express as a fraction in simplest form.

Answer 1

The probability of rolling two consonants on a cube with the letters S, O, L, V, E, D is calculated by multiplying the probability of rolling a consonant on one roll (2/3) by itself because the rolls are independent, resulting in a probability of 4/9.

Step-by-step explanation:

To calculate the probability of rolling two consonants with a cube having the letters S, O, L, V, E, D, we first need to determine the number of consonants and vowels. Here, the consonants are S, L, V, D, and the vowels are O and E. Thus, there are 4 consonants and 2 vowels.

Since each roll is independent and there are 6 sides to the cube, the probability of rolling a consonant on one roll is the number of consonants over the total number of sides, which is:

P(rolling a consonant) = 4/6 = 2/3

To find the probability of rolling two consonants in a row, we multiply the probability of rolling a consonant on the first roll by the probability of rolling a consonant on the second roll:

P(two consonants) = P(rolling a consonant) × P(rolling a consonant) = (2/3) × (2/3) = 4/9

Therefore, the probability of rolling two consonants in a row is 4/9.

Answer 2

There are 6 possible outcomes for each roll of the cube, since there are 6 letters on the cube. Out of the 6 letters, there are 3 consonants (S, L, V) and 3 vowels (O, E, D).

To find the probability of rolling two consonants, we need to multiply the probability of rolling a consonant on the first roll (3/6) by the probability of rolling a consonant on the second roll (also 3/6), since the rolls are independent events.

(3/6) * (3/6) = 9/36 = 1/4

Therefore, the probability of rolling two consonants is 1/4, which can also be expressed as 25%.