Question

a. Mary thinks of a number from 1 to 9 and John tries to guess it. Set up a sampled space and compute the probability that John’s guess is correct.

b. Independent filps of a coin that lands on heads with probability p are made. What is the probability that the first four outcomes are

(a) H, H, H, H?

(b) T, H, H, H?

(c) What is the probability that the pattern T,H,H,H occurs before the pattern H,H,H,H?

Hint for part (c): How can the pattern H,H,H,H occur first?

Answer 1

a)

sample space ={ 1,2,3,4,5,6,7,8,9 }

john guesses anyone out of this

so, probability that john guess is correct is = 1 / 9

b)

P(H) = p and P(T) = 1 - p

a) Prob ( H, H, H, H ) = P(H)P(H)P(H)P(H) = p^4

b) Prob ( T, H, H, H ) = P(T)P(H)P(H)P(H) = ( 1 - p ) p^3

c) Here, HHHH can only occur before THHH only if the fiirst four flips are HHHH.( because if T occur in any of the first four flips then HHHH cannot accur before THHH)

Prob( HHHH before THHH) = prob( HHHH) = p^4

therefore prob( THHH accurs before HHHH ) = 1 - P^4