Question

A coin is tossed 10 times. True or false, and explain: (a) The chance of getting 10 heads in a row is 1/1,024. (b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is 1/2.

Answer 1

a and b both are true.

Explanation:

Given : A coin is tossed 10 times.

To find : True or false, and explain ?

Solution :

(a) The chance of getting 10 heads in a row is
`(1)/(1024)`

Coin has two face head and tail.

The probability of getting head is
`P(H)=(1)/(2)`

The probability of getting 10 heads in a row is

`P=(P(H))^(10)`

`P=((1)/(2))^(10)`

`P=(1)/(1024)`

The chance of getting 10 heads in a row is
`(1)/(1024)` is true.

(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is
`(1)/(2)`.

The probability of getting 10 heads in a row is
`P_1=((1)/(2))^(10)`

The probability of getting 9 tosses were heads is
`P_2=((1)/(2))^(9)`

Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is given by,

`P=(P_1)/(P_2)`

`P=(((1)/(2))^(10))/(((1)/(2))^(9))`

`P=((1)/(2))^(10-9)`

`P=(1)/(2)`

Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is
`(1)/(2)` is true.