a fruit basket contains 10 mangoes, 8 bananas, and 2 oranges. If we picked 6 mangoes in 10 trials from the fruit basket, what would be the experimental probability?
prob of mango = 10/20 = 1/2
prob not a mango = 1/2
prob of 6 mangos out of 10
= C(10,6) (1/2)^6 (1/2)^4
= 210 (1/1024) = 210/1024 = 105/512
P of M = 10/20 (50%)
P of 6M =10/120 (8.33333%)
OR...
10F = 8+2 \ 1/\/\ o/
10M = 10 / 1\/\/ /o
P of M = 1/2
P of 6m = (1/2) / 6 = 1/12
To find the experimental probability, we need to divide the number of favorable outcomes (picking 6 mangoes) by the total number of trials (10).
First, let's find the total number of favorable outcomes (picking 6 mangoes). Since the fruit basket initially contains 10 mangoes, the number of favorable outcomes is determined by choosing 6 mangoes out of 10. This can be calculated using the combination formula, which is denoted as nCr.
The combination formula nCr is given by:
nCr = n! / (r! * (n-r)!)
In this case, n (the total number of mangoes) is 10, and r (the number of mangoes we want to pick) is 6.
So, applying the combination formula, we have:
10C6 = 10! / (6! * (10-6)!)
= (10 * 9 * 8 * 7 * 6!) / (6! * 4 * 3 * 2 * 1)
= 10 * 9 * 8 * 7 / (4 * 3 * 2 * 1)
= 210
Therefore, the total number of favorable outcomes is 210.
Now, we'll divide the number of favorable outcomes (210) by the total number of trials (10) to find the experimental probability:
Experimental probability = Number of favorable outcomes / Total number of trials
= 210 / 10
= 21
So, the experimental probability of picking 6 mangoes in 10 trials would be 21.
To find the experimental probability, we need to divide the number of successful outcomes (picking 6 mangoes) by the total number of trials (10 trials).
First, let's calculate the total number of possible outcomes. Since there are 10 mangoes, 8 bananas, and 2 oranges in the basket, the total number of fruits is 10 + 8 + 2 = 20.
Now, let's calculate the number of successful outcomes, which is picking 6 mangoes. Since there are 10 mangoes in the basket, we can calculate the number of ways to select 6 mangoes using combinations. The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen. In this case, n = 10 and r = 6. So, the number of ways to select 6 mangoes is 10C6 = 10! / (6! * (10-6)!) = 210.
Finally, we can calculate the experimental probability by dividing the number of successful outcomes by the total number of trials. Therefore, the experimental probability of picking 6 mangoes in 10 trials is 210/10 = 21.
So the experimental probability is 21.