A fair dice with face numbered 1,2,3,4,5,6 is thrown twice.what is the probability of obtaining a prime from each throw
To find the probability of obtaining a prime on each throw of a fair dice, we first determine the number of favorable outcomes and the total number of possible outcomes.
For the first throw, the favorable outcomes are 2, 3, and 5, as these are the prime numbers less than or equal to 6. Since there are 3 favorable outcomes, the probability of obtaining a prime on the first throw is 3/6 or 1/2.
Similarly, for the second throw, the favorable outcomes are also 2, 3, and 5. Again, there are 3 favorable outcomes, so the probability of obtaining a prime on the second throw is also 1/2.
Since the outcomes of each throw are independent events, we can multiply the probabilities of each throw to find the overall probability. Therefore, the probability of obtaining a prime from each throw is:
(1/2) * (1/2) = 1/4
So, the probability of obtaining a prime from each throw is 1/4 or 0.25.
To find the probability of obtaining a prime number from each throw of a fair dice, we need to determine the total number of outcomes in which a prime number can be obtained, as well as the total number of possible outcomes.
1. Total number of possible outcomes: The fair dice has 6 faces, so there are a total of 6 possible outcomes for each throw. Therefore, the total number of possible outcomes for two throws is 6 * 6 = 36.
2. Prime numbers on a dice: The prime numbers that can be obtained from a dice are 2, 3, and 5. These numbers are found on the faces numbered 2, 3, and 5.
3. Prime numbers on the first throw: The probability of obtaining a prime number on the first throw is 3/6, since there are 3 prime numbers out of the 6 possible outcomes.
4. Prime numbers on the second throw: Similarly, the probability of obtaining a prime number on the second throw is also 3/6.
5. Probability of obtaining a prime number on each throw: To find the probability of obtaining a prime number on each throw, we multiply the probabilities from the first and second throw together:
(3/6) * (3/6) = 9/36 = 1/4.
Therefore, the probability of obtaining a prime number from each throw of a fair dice is 1/4 or 25%.