Question

If you roll 2 dice, what is the probability that you will roll a seven (the numbers on the dice add up to a seven) on or before the 5th roll

Answer 1

1+2+3+4+5+6=21
21+21=42
3/42=1/14
Answer 1/14

Answer 2

The probability of rolling a seven on or before the 5th roll is 5/6 or about 83.3%

Explanation:

The probability of rolling a seven on any given roll of two dice is 1/6, since there are six ways to roll a seven (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of the 36 possible outcomes (1-6 on the first die and 1-6 on the second die).

To find the probability of rolling a seven on or before the 5th roll, we can use the cumulative probability formula which is the probability of getting a specific event on the first roll plus the probability of getting the event on the second roll plus the probability of getting the event on the third roll and so on.

So the probability of rolling a seven on or before the 5th roll is:

P(rolling a seven on the 1st roll) + P(rolling a seven on the 2nd roll) + P(rolling a seven on the 3rd roll) + P(rolling a seven on the 4th roll) + P(rolling a seven on the 5th roll)

= (1/6) + (1/6) + (1/6) + (1/6) + (1/6)

= 5/6

So the probability of rolling a seven on or before the 5th roll is 5/6 or about 83.3%

It's worth noting that this probability is independent of the previous outcomes of the rolls, so the probability of rolling a seven on or before the 5th roll stays the same even if you already rolled a seven in previous rolls.