Question

Find the probability of at least three successes in six trials of a binomial experiment in which the probability of success is 50%. Round to the nearest tenth of a percent. Please help me ASAP!!!

Answer 1

Answer:

31.3%

Step-by-step explanation:

Start by doing the binomial expansion of (x+y)^6 where x represents success. This is  

(x^6y^0) + 6(x^5y^1) +15(x^4y^2) +20(x^3y^3) +15(x^2y^4) +6(x^1y^5) +(x^0y^6)  

We are interested in the x^3y^3 term which represents exactly 3 successes. Since the probability of success and failure are both .5 we should be able to figure this out just using the coefficients of the terms which is  

20/64 = .3125 which is 31.25% Rounding yo the nearest tenth gives us

Answer 2

Start by doing the binomial expansion of (x+y)^6 where x represents success. This is

(x^6y^0) + 6(x^5y^1) +15(x^4y^2) +20(x^3y^3) +15(x^2y^4) +6(x^1y^5) +(x^0y^6)

We are interested in the x^3y^3 term which represents exactly 3 sucesses. Since the probalbility of sucess and failure are both .5 we should be able to figure this out just using the coefficients of the terms which is

20/64 = .3125 which is 31.25%

by rounding off,we can say that the answer is 31.30