AP EAMCET201822 Apr 2018Morning ShiftMathematicsProbabilityActual

If X is a binomial variate with mean 6 and variance 2 , then the value of P(5 X 7) is

Options

A4762 6561
B4672 6561
C5264 6561
D5462 6651

Correct answer

B. 4672 6561

Step-by-step solution

We have, aligned & n p=6 and n p q=2 & 6 q=2 & q= 1 3 & p=1-q=1- 1 3 = 2 3 & n 2 3 =6 & n=9 & P(5 x 7)=P(x=5)+P(x=6)+P(x=7) & = ^9 C₅ ( 2 3 )^5 ( 1 3 )^4+ ^9 C₆ ( 2 3 )^6 ( 1 3 )^3+ ^9 C₇ ( 2 3 )^7 ( 1 3 )^2 & = 1 3^9 [ 9 8 7 6 4 3 2 1 32+ 9 8 7 3 2 1 64+ 9 8 2 1 128 ] & = 1 3^9 [9 8 7 2 4+3 8 7 32+9 4 128] & = 3 8 7 2 4+8 7 32+3 4 128 3^8 & = 1344+1792+1536 6561 = 4672 6561 . & aligned

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