The random variable X has Binomial distribution B (20,0.4) . Then 5-5 P ( X 2)=

Step-by-step solution

Given X is a random variable with B (20,0.4) . So, x=20, P=0.4= 4 10 = 2 5 . Then, q=1- P =1- 2 5 = 3 5 . Now, aligned & 5-5 P ( X 2)=5-5(1-( P ( X =0)+ P ( X =1))) & =5- (1- ( ²⁰ c ₀ P ^0 q ²⁰+ ²⁰ c ₁ P ^1 q ¹⁹ ) ) & =5-5 [1- (1 ( 1 5 )^0 ( 3 5 )²⁰+20 ( 2 5 )^1 ( 3 5 )¹⁹ ) ] & =5-5 [1- ( ( 3 5 )²⁰+8 ( 3 5 )¹⁹ ) ] & =5-5 [1- ( 3 5 )¹⁹ ( 3 5 +8 ) ] & =5-5 [1- ( 3 5 )¹⁹ 43 5 ] & =5 ( 3 5 )¹⁹ 43 5 =43 ( 3 5 )¹⁹ aligned