In a binomial experiment with and . Find
0.0003
0.0025
0.0807
0.1264
0.1875
To find these probabilities in a binomial experiment, we can use the binomial probability formula:
P(x) = (n choose x) * p^x * q^(n-x)
Where:
- n is the number of trials
- x is the number of successes
- p is the probability of success in a single trial
- q is the probability of failure in a single trial (q = 1 - p)
Given values:
n = 8
p = 0.5
q = 0.5 = 1 - 0.5 = 0.5
Now, we can find the individual probabilities:
1. P(x=3) = (8 choose 3) * 0.5^3 * 0.5^(8-3) = 56 * 0.5^3 * 0.5^5 = 0.21875
2. P(x=5) = (8 choose 5) * 0.5^5 * 0.5^(8-5) = 56 * 0.5^5 * 0.5^3 = 0.21875
3. P(x=6) = (8 choose 6) * 0.5^6 * 0.5^(8-6) = 28 * 0.5^6 * 0.5^2 = 0.10938
4. P(x=7) = (8 choose 7) * 0.5^7 * 0.5^(8-7) = 8 * 0.5^7 * 0.5^1 = 0.03125
5. P(x=8) = (8 choose 8) * 0.5^8 * 0.5^(8-8) = 1 * 0.5^8 * 0.5^0 = 0.00391
Therefore, the probabilities are:
- P(x=3) = 0.21875
- P(x=5) = 0.21875
- P(x=6) = 0.10938
- P(x=7) = 0.03125
- P(x=8) = 0.00391
None of the given values match exactly with the calculated probabilities.