Jim rolled a fair die 5 times and obtained a 3 every time.
He concluded that on the next roll, a 3 is more likely to
occur than the other numbers. Explain whether this is
true.
If it is a "fair die," the probability of any one number is always 1/6.
http://www.members.cox.net/dagershaw/lol/Odds.html
To determine whether Jim's conclusion is true, we need to understand the concept of probability and independence of events. When a fair die is rolled, each number (1, 2, 3, 4, 5, or 6) has an equal chance of appearing, which is 1/6 or approximately 16.67%.
In Jim's case, he rolled the die 5 times and got a 3 every time. However, it's important to note that each roll of the die is an independent event. This means that the outcome of one roll does not affect the outcome of subsequent rolls. So, even if Jim got a 3 on the first 5 rolls, the probability of getting a 3 on the next roll remains the same at 1/6 or approximately 16.67%.
The probability of getting a 3 on any single die roll is not influenced or altered by previous outcomes. Each roll is a separate event, and the probability remains constant for each number on the die.
Therefore, Jim's conclusion that a 3 is more likely to occur on the next roll is not true. The probability of getting a 3 on the next roll is the same as any other number, 1/6 or approximately 16.67%.