7 coins are tossed simultaneously . What is the probability that a tail appears an odd number of times ?

Answer

`(1)/(2)`

Explanation

7 coins being tossed simultaneously is the same as one coin being tossed 7 times .
`:. , p =(1)/(2) , q=(1)/(2) " and " n=7`
Let X show the number of tails .Then
`P(X=r) =.^(n)C_(r ) .p^(r ) .q^((n-r)) =.^(7)C_(r ) .((1)/(2))^(7)`
Required probability `P(X=1)+P(x=3)+ P(X=5) +P(X=7)`