Probability Rules and Expected Values

Feedback: Not quite! There are 10 yellow balls out of a total of 50. The probability of drawing a yellow ball is $\frac{10}{50}$, which simplifies to $\frac{1}{5}$.

Feedback: Not quite! There are two favourable outcomes (rolling a 2 or a 6) out of 6 possible outcomes. Therefore, the probability is $\frac{2}{6}$, which simplifies to $\frac{1}{3}$.

Feedback: Not quite! The total number of red and green marbles is 15 (red) + 10 (green) = 25 marbles. The total number of marbles is 30. The probability of drawing a red or green marble is $\frac{25}{30}$, which simplifies to $\frac{5}{6}$.

Feedback: Not quite! The total number of yellow and blue marbles is 4 (blue) + 2 (yellow) = 6 marbles. The total number of marbles is 12. So, the probability of drawing a yellow or blue marble is $\frac{6}{12}$, which simplifies to $\frac{1}{2}$.

Feedback: Not quite! The probability of rolling a 3 on a fair die is $\frac{1}{6}$. If you roll the die 60 times, the expected number of 3s is $\frac{1}{6} \times 60 = 10$.

Feedback: Not quite! The probability of rolling a number less than 3 (either 1 or 2) is $\frac{2}{6}$, or $\frac{1}{3}$. If you roll the die 120 times, you would expect to roll a number less than 3 about 40 times, because the probability of rolling a number less than 3 is $\frac{1}{3}$, and $\frac{1}{3} \times 120 = 40$.