a pair of dice is thrown ...find the probability of getting 7 as the sum if it is knwn that second die is always exihibts a prime number
second die : 2,3,5
to get 7, must be 5,4,2
probability = likely outcomes / all outcomes
i think it is 1/2 - don't trust me not a reliable source
r s k v east vinod nagar
To find the probability of getting a sum of 7 when throwing a pair of dice, given that the second die always exhibits a prime number, we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the favorable outcomes:
The possible sums that can be obtained when throwing a pair of dice range from 2 to 12. However, since we know that the second die is always a prime number, we can exclude the cases where the second die shows 2, 3, 5, or 7, as they are not prime. That leaves us with 11 possible sums: 3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15.
Next, let's calculate the total number of possible outcomes:
When throwing two dice, each die has 6 possible outcomes (numbers 1 to 6), so the total number of possible outcomes for a pair of dice is 6 * 6 = 36.
Now we can calculate the probability:
The probability of an event is the number of favorable outcomes divided by the number of possible outcomes.
In this case, the number of favorable outcomes is 11 and the total number of possible outcomes is 36.
Therefore, the probability of getting a sum of 7 when the second die always exhibits a prime number is 11/36, which is approximately 0.3056 or 30.56%.
Remember that this probability assumes a fair pair of dice where each outcome is equally likely.