Eyes nepal. The way you think is absolutely right and you are almost there . But you completely ignoring  the number of toss. 

Mero sano dimag le nikalya answer chahi    0.47   ho.  I may be wrong.

let me explain how i came to this.

n is number of tries  = 10
r is chance of getting
Probablity of head in each toss P(H) = 0.3
Probablity of tais in each toss P(T) = 0.7

Probablity of getting 2 Heads  P (2H)  =  n C r  *  (0.3) power 2  * (0.7) power 8
                                                          =  10 C 2 * (0.3) power 2  * (0.7) power 8
                                                           =0.233

probablity of getting 4 Heads P(4H)=  10 C 4 *  (0.3) power 4 * (0.7) power 6
                                                      = 0.200

P(6H)=   10C6 *  (0.3) power 6  * (0.7) power 4
P (8H)=   10 C r8 *  (0.3) power 8  * (0.7) power 2
P(10H) = 10 C 10  *  (0.3) power 10  * (0.7) power 0

Now add everything = P(2H)+P(4H)+P(6H)+P(8H)+P(10H)
                                = 0.47

I may be wrong though. But this is what i came.