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 with n=10 and p=0.3:
1. P(X=3) = 10C3 * (0.3)^3 * (0.7)^7 = 120 * 0.027 * 0.082354 = 0.2636
2. P(X=5) = 10C5 * (0.3)^5 * (0.7)^5 = 252 * 0.00243 * 0.16807 = 0.0807
3. P(X<3) = P(X=0) + P(X-1) + P(X=2) = 0.028 = 0.0003
4. P(X>7) = P(X=8) + P(X=9) + P(X=10) = 0.0059
5. P(X≥4) = P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10) = 0.8128
Therefore, the probabilities for the given values are:
1. 0.2636
2. 0.0807
3. 0.0003
4. 0.0059
5. 0.8128