The probability that at most 3 tosses of a balanced dice are required to get a prime number on top is equal to????
To find the probability that at most 3 tosses of a balanced dice are required to get a prime number on top, we need to find the probability of getting a prime number in 1, 2, or 3 tosses.
First, let's determine the sample space. A balanced dice has 6 possible outcomes (numbers 1 to 6) when rolled.
Next, let's find the favorable outcomes, i.e., the prime numbers. The prime numbers on a balanced dice are 2, 3, and 5.
Now, let's calculate the probability of getting a prime number on top in each toss:
- The probability of getting a prime number on the first toss is 3/6, since there are 3 favorable outcomes (prime numbers) out of the total 6 outcomes (sample space).
- Similarly, the probability of getting a prime number on the second toss is also 3/6, as each toss is independent.
- Finally, the probability of getting a prime number on the third toss is still 3/6.
Since we are looking for the probability of getting a prime number in at most 3 tosses, we need to find the complement of the event "not getting a prime number in 3 tosses." In other words, we calculate the probability of not getting a prime number in any of the 3 tosses and subtract it from 1.
To calculate the probability of not getting a prime number in any of the 3 tosses:
- The probability of not getting a prime number on the first toss is 3/6.
- Similarly, the probability of not getting a prime number on the second toss is 3/6.
- Finally, the probability of not getting a prime number on the third toss is also 3/6.
To find the cumulative probability of not getting a prime number in any of the 3 tosses, we multiply the probabilities together:
(3/6) * (3/6) * (3/6) = (1/2) * (1/2) * (1/2) = 1/8.
To find the probability of getting a prime number in at most 3 tosses, we subtract the probability of not getting a prime number in 3 tosses from 1:
1 - 1/8 = 7/8.
Therefore, the probability that at most 3 tosses of a balanced dice are required to get a prime number on top is 7/8.