Riley is playing a game that requires rolling a number cube numbered 1-6 and spinning a spinner with 3 consonants and 1 vowel. The sections of the spinner are all the same size. What is the probability that Riley rolls a number less than 3 and lands on a consonant?

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Question:

Riley is playing a game that requires rolling a number cube numbered 1-6 and spinning a spinner with 3 consonants and 1 vowel. The sections of the spinner are all the same size. What is the probability that Riley rolls a number less than 3 and lands on a consonant?

A: 3/8 B: 1/12 C:1/8 D:1/4

Answer:

Using the principle of independent probability, the probability of the event is 1/4

Sample space :

  • Number cube = (1, 2, 3, 4, 5, 6)
  • Spinner = (c, c, c, v)

Recall :

  • Probability = required outcome / Total possible outcomes

1.) Probability of number less than 3 and a constant :

Numbers less than 3 = (1, 2)

  • P(Number < 3) = 2 / 6 = 1/3
  • P(consonant) = 3 / 4

P(number < 3 and constant) = 1/3 × 3/4 = 3/12 = 1/4

Therefore, the probability of the event is 1/4

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