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: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.