two un biasedtetrahedral dice each have four faces number 1,2,3 and 4. the two dices are thrown together and the sum of the numbers on the faceson which they land is noted. Find the expected number of occasions on which the sum is 7 or more when the dice are thrown together 200 times.
To find the expected number of occasions on which the sum is 7 or more when the dice are thrown together 200 times, we need to calculate the probability of getting a sum of 7 or more on a single throw, and then multiply it by the number of throws.
First, let's find the probability of getting a sum of 7 or more on a single throw. We can do this by counting the number of favorable outcomes and dividing it by the total number of possible outcomes.
For a sum of 7 or more, there are three possible outcomes:
1. (4,4) - Both dice show 4.
2. (4,3), (3,4) - One die shows 4, the other shows 3.
3. (4,2), (2,4), (3,3) - One die shows 4, the other shows a number less than 4.
The total number of possible outcomes is 4 x 4 = 16 since each die has 4 sides.
So, the probability of getting a sum of 7 or more on a single throw is (3 + 2 + 3)/16 = 8/16 = 1/2.
Now, let's calculate the expected number of occasions. We multiply the probability of getting a sum of 7 or more on a single throw (1/2) by the number of throws (200).
Expected number of occasions = (1/2) x 200 = 100.
Therefore, the expected number of occasions on which the sum is 7 or more when the dice are thrown together 200 times is 100.