10 coins are tossed simultaneously . Find the probability of getting
(i) exactly 3 heads (ii) not more than 4 heads
(iii) at least 4 heads .

Answer

`(i).(15)/(128) (ii) .(193)/(512) (iii) .(53)/(64)`

Explanation

10 coins being tossed simultaneously is the same as one coin being tossed 10 times
`P(X =r) =.^(n)C_(r ) .p^(r ).q^((n-r)) =.^(10)C_(r ) .((1)/(2))^(10)`
(i) P( exactly 3 heads ) `=.^(10)C_( 3) .((1)/(2))^(10)`
(ii) P (not more that 4 heads)
`=P(X le 4)` ltbgt ` =P(X =0) +P(X=1)+ P(X=2) +P(X =3) +P(X=4)`
`=(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2) +.^(10)C_(3)) .((1)/(2))^(10)`