Mean (m) for BD=np and variance (σ2) for BD=npq Given, np+npq=2.7 and n=3 ∴np(1+q)=2.7⇒p(1+q)=
2.7
3
⇒p(1+q)=0.9 ⇒(1−q)(1+q)=0.9 [∵ for BD probability standard deviation (SD), p+q=1 ] ⇒1−q2=0.9 ⇒q2=0.1⇒q=±0.3 ∴q=0.3 [∵q=−0.3 can't possible as 0≤q≤1] ⇒p=0.7 and q=0.3 ∴B.D. =(0.3+0.7)5 Hence, option (b) is correct.