A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event.
One die shows a 5, and the other is a number less than 2.
1/6 that the dice will roll a 5.
1/6 that the dice will roll a number less than 2.
1/3
To find the probability of this event, we need to determine how many outcomes satisfy the given condition and divide it by the total number of possible outcomes.
There are 6 possible outcomes for each of the two dice, giving us a total of 6 * 6 = 36 possible outcomes.
Out of these 36 outcomes, there is only one outcome where one die shows a 5 (5, 1) and the other is a number less than 2 (1). Therefore, the number of outcomes that satisfy the given condition is 1.
Thus, the probability of one die showing a 5 and the other being a number less than 2 is 1/36.
To find the probability of this event, we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the favorable outcomes. We are given that one die shows a 5. So, the favorable outcomes are when the other die is a number less than 2, which means it can be either 1 or nothing (since it cannot be negative).
Next, let's determine the total number of possible outcomes. When two dice are rolled, each die has 6 possible outcomes (numbers 1 to 6). Therefore, the total number of possible outcomes is 6 multiplied by 6, which equals 36.
Now, let's calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Since there is only one favorable outcome (one die showing a 5 and the other die being a number less than 2), we have:
Probability = 1 / 36
Hence, the probability of the event is 1/36.