Final answer:
The expected number of times a 3 will be rolled when a biased six-sided die is rolled 10 times is 60/13, denoting how frequently we anticipate the event of rolling a 3 due to the weighted nature of the die. Option b.
Step-by-step explanation:
The student is asking about the expected value of a certain outcome when rolling a weighted six-sided die multiple times. In this case, the die is biased so that a 3 is rolled with a higher probability than the other numbers. Specifically, the probability of rolling a 3 is given as 6/13 on average.
When rolling the die 10 times, we calculate the expected number of times a 3 will come up by multiplying the probability of rolling a 3 by the number of rolls.
To find the expected number of times a 3 is rolled in 10 rolls, we use the following formula:
Expected Value (E) = Number of trials (n) * Probability (p)
E = 10 * (6/13)
E = 60/13
Therefore, the expected number of times a 3 will be rolled in 10 tries is 60/13, which corresponds to option (b).