To solve this problem, we need to calculate the probability of two independent events occurring one after the other. Here are the details given:
1. Event A: A coin toss results in heads.
2. Event B: A number cube (standard six-sided die) lands on any number from 1 to 6.
### Step-by-Step Solution
1. Calculate the probability of Event A (coin toss is heads):
- A fair coin has two possible outcomes: heads or tails.
- Therefore, the probability of getting heads when flipping the coin is:
[tex]\[
P(\text{Heads}) = \frac{1}{2} = 0.5
\][/tex]
2. Calculate the probability of Event B (number cube shows any specific number):
- A standard number cube has six faces, each showing a different number from 1 to 6.
- The probability of rolling any specific number (e.g., rolling a 1) is:
[tex]\[
P(\text{any specific number}) = \frac{1}{6} \approx 0.1667
\][/tex]
3. Calculate the combined probability of both events occurring:
- Since flipping a coin and rolling a number cube are independent events, the probability of both events occurring together is the product of their individual probabilities.
- Therefore, the combined probability [tex]\( P(A \text{ and } B) \)[/tex] is:
[tex]\[
P(A \text{ and } B) = P(\text{Heads}) \times P(\text{any specific number})
\][/tex]
[tex]\[
P(A \text{ and } B) = 0.5 \times 0.1667 \approx 0.0833
\][/tex]
So, the probabilities are:
- The probability of getting heads: [tex]\( 0.5 \)[/tex]
- The probability of rolling any specific number: [tex]\( 0.1667 \)[/tex]
- The combined probability of getting heads and rolling any specific number: [tex]\( 0.0833 \)[/tex]
This solution explains how each probability is calculated and how they combine to give the final result.
