Question

9. [12pts: 3pts each] It is estimated that 7 centers that cannot be detected until the tangerines are cut open. The of 8 What is the probability of geting at least two good tangerines in a 096 ofa tangerine crop is good; the other 30% have rotten Chace at leass z 8oos tunyes Sucx 3 What is the probability of getting less than six good tangerines in a sack? 4790 Chance of good burger Mes 309.

Answer 1

$p=70\%=0.7,n=8$

Let $q=1-p=0.3$

$P(X=x)=n_{C_{x}}(q)^{n-x}(p)^{x}$

a) $P(X\geq 2)=1-P(X=0)-P(X=1)$

$=1-8_{C_{0}}(0.3)^{8-0}(0.7)^{0}-8_{C_{1}}(0.3)^{8-1}(0.7)^{1}$

$=1-(0.3)^{8}-8(0.3)^{7}(0.7)$

$=0.9987$

b)

   $=1-28(0.3)^{2}(0.7)^{6}-8(0.3)(0.7)^{7}-(0.7)^{8}$

$=0.4482$