If an event
A.implies obtaining prime number of an event
B.implies obtaining an odd number in a single throw of a dice. Find the probability of event A or B.
To find the probability of event A or B, we need to find the probabilities of each event individually and then sum them up, while accounting for any overlap in the outcomes.
Let's start by finding the probability of event A, which is obtaining a prime number in a single throw of a dice.
A prime number is a number greater than 1 that is only divisible by 1 and itself. In the case of a standard six-sided dice, the possible outcomes are numbers 1 to 6.
To determine the prime numbers in this range, we find that 2, 3, and 5 are the only prime numbers. Therefore, the event A consists of getting a 2, 3, or 5. These outcomes have no overlap with event B since none of them are odd numbers.
Since each outcome on a fair dice has an equal probability of 1/6, the probability of event A is 3/6 or 1/2 (since there are 3 favorable outcomes out of 6 possible outcomes).
Now let's find the probability of event B, which is obtaining an odd number in a single throw of a dice.
The odd numbers on a standard six-sided dice are 1, 3, and 5. Again, these outcomes do not overlap with event A since none of them are prime numbers.
The probability of event B is 3/6 or 1/2 (since there are 3 favorable outcomes out of 6 possible outcomes).
To find the probability of event A or B, we need to sum up the individual probabilities of A and B, while accounting for any overlap. However, since A and B have no overlap, we can simply add their probabilities:
Probability of event A or event B = Probability of event A + Probability of event B
= 1/2 + 1/2
= 1
Therefore, the probability of event A or event B is 1 or 100%.
Note: The events A and B are mutually exclusive, meaning that they cannot happen at the same time. Thus, the probability of either A or B occurring is the sum of their individual probabilities.