Answer :
Sure! Let's solve the problem step-by-step:
1. Probability of rolling a 1 or 6 on a number cube:
- A number cube (commonly known as a six-sided die) has 6 faces, numbered 1 through 6.
- The probability of rolling a specific number (such as 1) is \(\frac{1}{6}\).
- Since there are two desired outcomes (rolling a 1 or rolling a 6), the combined probability is \(\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}\).
2. Probability of flipping tails on a coin:
- A coin has 2 faces: heads and tails.
- The probability of flipping tails is \(\frac{1}{2}\).
3. Combined probability of both events happening:
- The combined probability of two independent events happening is the product of their individual probabilities.
- Thus, the combined probability is:
[tex]\[ \left(\frac{1}{3}\right) \times \left(\frac{1}{2}\right) = \frac{1}{6} \][/tex]
Therefore, the probability of rolling a 1 or 6 on a number cube and flipping tails on a coin is \(\frac{1}{6}\).
Thus, the correct answer is:
D) [tex]\(\frac{1}{6}\)[/tex]
1. Probability of rolling a 1 or 6 on a number cube:
- A number cube (commonly known as a six-sided die) has 6 faces, numbered 1 through 6.
- The probability of rolling a specific number (such as 1) is \(\frac{1}{6}\).
- Since there are two desired outcomes (rolling a 1 or rolling a 6), the combined probability is \(\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}\).
2. Probability of flipping tails on a coin:
- A coin has 2 faces: heads and tails.
- The probability of flipping tails is \(\frac{1}{2}\).
3. Combined probability of both events happening:
- The combined probability of two independent events happening is the product of their individual probabilities.
- Thus, the combined probability is:
[tex]\[ \left(\frac{1}{3}\right) \times \left(\frac{1}{2}\right) = \frac{1}{6} \][/tex]
Therefore, the probability of rolling a 1 or 6 on a number cube and flipping tails on a coin is \(\frac{1}{6}\).
Thus, the correct answer is:
D) [tex]\(\frac{1}{6}\)[/tex]
