A pack of cards consists of 15 cards numbered 1 to 15. Three cards are drawn at random with replacement. Then, the probability of getting 20 odd and one even numbered cards is

$\frac{448}{1125}$

Let $Ę_i$ (i=1, 2, 3) denote the event of drawing an even numbered card in ith draw and O; denote the event of drawing an odd numbered card ini th (i =1, 2, 3) draw. Then,

Required probability

$= P((E_1∩O_2∩O_3) U(O_1∩ E_2∩ O_3) U(O_1 ∩ O_2 ∩E_3)]$

$= P(E_1∩ O_2∩O_3) + P(O_1∩ E_2O_3) + P(O_1∩O_2 ∩E_3)$

$= P(E_1) P(O_1) P(O_3) + P(O_1) P(E_2) P(O_3) + P(O_1) P(O_2) P(E_3)$

$=\frac{7}{15}× \frac{8}{15} ×\frac{8}{15} + \frac{8}{15} ×\frac{7}{15}  × \frac{8}{15} +\frac{8}{15}  ×\frac{8}{15}   × \frac{7}{15}  $

$=\frac{3×7 × 8^2}{15^3}=\frac{448}{1125}$