Question

Using a standard six-sided die, Janice rolled either a 2 or a 5 on the last 6 rolls of the die. What is the probability of Janice rolling a 2 or a 5 on her 7th toss of the die?

a. 1/3
b. 1/6
c. 2/7
d. 1/7

Answer 1

The probability of Janice rolling either a 2 or 5 on her 7th toss of a six-sided die is 1/3, consistent with option (a), as each die roll is an independent event, and there are two favorable outcomes out of six possible. The correct answer is option a.

Step-by-step explanation:

The student asked what the probability of Janice rolling either a 2 or a 5 is on her 7th toss of a standard six-sided die. Having rolled either a 2 or a 5 on the last 6 rolls is irrelevant to the next roll's outcome due to the die's lack of memory. The probability of any single event is not influenced by the previous outcomes because each roll is an independent event.

In a fair six-sided die, the sample space S is {1, 2, 3, 4, 5, 6}. The event of rolling a 2 or a 5 has two favorable outcomes in this sample space. To calculate the probability of Janice rolling a 2 or a 5, we count the number of favorable outcomes for the event E (rolling a 2 or 5) and divide it by the total number of possible outcomes in the sample space:

P(E) = Number of favorable outcomes for E / Total number of possible outcomes in S

P(E) = 2 / 6 = 1/3

Therefore, the correct answer to the probability of Janice rolling a 2 or a 5 on her 7th toss is 1/3, which corresponds to option (a).