A pair of fair dice is tossed 3 times.
Find the probability a seven appears 3 times.
On a single toss of a pair of dice, the probability of getting a seven are 1/6.
For three consecutive tosses of 7, the probability is (1/6)^3 = 1/216
To find the probability of a seven appearing 3 times when a pair of fair dice is tossed 3 times, we can use the concept of independent events.
Step 1: Determine the total number of possible outcomes.
Since we are tossing a pair of fair dice 3 times, each dice can have 6 possible outcomes (numbers 1 to 6). As there are 2 dice, the total number of possible outcomes is 6 x 6 = 36.
Step 2: Determine the number of favorable outcomes.
To have a seven appear 3 times, both dice must show a value of 1, which is the only combination that sums up to 7.
So, there is only 1 favorable outcome for each toss. Since we are tossing the dice 3 times, the number of favorable outcomes is 1 x 1 x 1 = 1.
Step 3: Calculate the probability.
The probability of an event occurring is defined as the number of favorable outcomes divided by the number of total possible outcomes.
So, the probability of a seven appearing 3 times is 1 (number of favorable outcomes) / 36 (number of total possible outcomes).
Therefore, the probability of a seven appearing 3 times when a pair of fair dice is tossed 3 times is 1/36.
To find the probability that a seven appears three times when a pair of fair dice is tossed three times, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
To get a seven on two dice, there are six possible combinations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). These are the only ways to get a sum of seven.
Since we have three tosses, we need to calculate the probability of getting a seven on each toss and then multiply the probabilities together.
The probability of getting a seven on each toss is 6/36, or 1/6, since there are six possible combinations out of a total of 36 outcomes.
Therefore, the probability of getting a seven on all three tosses is:
(1/6) * (1/6) * (1/6) = 1/216
So, the probability that a seven appears three times is 1/216.