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

Answer:

a and b both are true.

Step-by-step 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 $\frac{1}{1024}$

Coin has two face head and tail.

The probability of getting head is $P(H)=\frac{1}{2}$

The probability of getting 10 heads in a row is

$P=(P(H))^{10}$

$P=(\frac{1}{2})^{10}$

$P=\frac{1}{1024}$

The chance of getting 10 heads in a row is $\frac{1}{1024}$ is true.

(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is $\frac{1}{2}$.

The probability of getting 10 heads in a row is $P_1=(\frac{1}{2})^{10}$

The probability of getting 9 tosses were heads is $P_2=(\frac{1}{2})^{9}$

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

$P=\frac{P_1}{P_2}$

$P=\frac{(\frac{1}{2})^{10}}{(\frac{1}{2})^{9}}$

$P=(\frac{1}{2})^{10-9}$

$P=\frac{1}{2}$

Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is $\frac{1}{2}$ is true.