Probability — Class 12 Maths Solution

.: When a dice is tossed thrice, the sample space is

$S = \{ (x,y,z):x,y,z \in \{ 1,2,3,4,5,6\} \}$

,which contains $6 \times 6 \times 6 = 216$

equally likely events.

Let $E:$ 'an odd number atleast once'

then ${E^c}:$ 'not an odd number any time'

i.e., ${E^c} =$ ’ an even number on all throws
'
or ${E^c} = \{ (x,y,z):x,y,z \in \{ 2,4,6\} \}$

$\Rightarrow$ contains $3 \times 3 \times 3 = 27$

equally likely simple events.

$\Rightarrow$ $P\left( {{E^c}} \right) = \cfrac{{27}}{{216}}$

$\therefore$

Required probability $= P(E) = 1 - P\left( {{E^c}} \right)$

$= 1 - \cfrac{{27}}{{216}} = 1 - \cfrac{1}{8} = \cfrac{7}{8}$