Respuesta :
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 [tex]\frac{1}{1024}[/tex]
Coin has two face head and tail.
The probability of getting head is [tex]P(H)=\frac{1}{2}[/tex]
The probability of getting 10 heads in a row is
[tex]P=(P(H))^{10}[/tex]
[tex]P=(\frac{1}{2})^{10}[/tex]
[tex]P=\frac{1}{1024}[/tex]
The chance of getting 10 heads in a row is [tex]\frac{1}{1024}[/tex] is true.
(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is [tex]\frac{1}{2}[/tex].
The probability of getting 10 heads in a row is [tex]P_1=(\frac{1}{2})^{10}[/tex]
The probability of getting 9 tosses were heads is [tex]P_2=(\frac{1}{2})^{9}[/tex]
Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is given by,
[tex]P=\frac{P_1}{P_2}[/tex]
[tex]P=\frac{(\frac{1}{2})^{10}}{(\frac{1}{2})^{9}}[/tex]
[tex]P=(\frac{1}{2})^{10-9}[/tex]
[tex]P=\frac{1}{2}[/tex]
Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is [tex]\frac{1}{2}[/tex] is true.
