Question

Bryan has been tossing coins and recording how many heads he gets. He knows that he got the 4th head on the 13th trial. What is the probability that he got the 3rd head on the 8th trial? 18 Tries 0/5

Answer 1

Solution - Givey, Bryan has been tossing coins and recording howmany heads he gets. Probability of Head P(H)=0.5. Probability of tail P(T) =0.5 Let us suppose A be the event the 4th head occurred in 18th trail P(A) is given the 4th head occures on the 13th trail if there are 3 heads in the first 12, And then a head. Using Binomial trail PLA) = (2) 4 () 2-3 (7) = 1263 (₂² (₂) Let B be the event the third head occured on 8th ferail. Meaus there are a heads in the first 7 trails & then a head P(6) = (2) G) 2 (3) (+) = 7a () 7 (²) Now, we need to find

13th trail). P(gold head on 8th trail 14th head on P(BIA) = P(AMB) P(A) Now, we will find P (ARB) Given that B happend, the probability of A is the probability that in coin tossing the first head occurs on the fifth trail This is just probability of TTTTH = ( ) ( ) ( ) (₂) (²) P (TTTTH)= (₂) This , P (ANB) = P(B). P(TTTTH) = 7a ( 2 (z) x (₂) =702 () Now calculate P(BIA) = P(ANB) P(A) 1223 (4) dez 27 (2-2)! 31 (12-2) 71 21 (7-2)! 121 12 C3

7- 215! 121 31 9% 318% 215! 12 ! got and in the probability that Bryan head on 8th trail = 21 10.095 220