Find the (theoretical) probability of a given event, assuming that the dice are distinguishable and fair, and that what is observed are numbers uppermost.
Two dice are rolled; the numbers add to 7.
1
The probability of rolling 7 with two dice is 1/6. Six of 36 possible equally likely outcomes yield a sum of 7.
1p
If a pair of dice are rolled, the probability that the sum of the numbers of dots appearing is 5 is
To find the theoretical probability of rolling a combined sum of 7 when two dice are rolled, let's break down the problem step by step.
Step 1: Understand the problem
The problem states that two dice are rolled, and we want to find the probability that the numbers on the upper sides of the dice add up to 7.
Step 2: Determine the possible outcomes
When rolling two distinguishable dice, each die has 6 possible outcomes, ranging from 1 to 6. Therefore, the total number of possible outcomes is 6 x 6 = 36.
Step 3: Find the favorable outcomes
To obtain a sum of 7, there are six possible combinations: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Out of the 36 possible outcomes, we have 6 favorable outcomes.
Step 4: Calculate the probability
The theoretical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. So, in this case, the probability can be expressed as:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 6 / 36
Probability = 1 / 6
Therefore, the theoretical probability of rolling a combined sum of 7 when two distinguishable and fair dice are rolled is 1/6 or approximately 0.1667.