Question

slader What is the conditional probability that a randomly generated bit string of length four contains at least two consecutive 0s, given that the first bit is a 1? (Assume that the probabilities of a 0 and a 1 are the same.)

Answer 1

Answer:

3/8

Step-by-step explanation:

total number in bit string of lent 4=16

let s be the set of all bit strings of length 4

the probability tat an event is randomly selected is A

that an event is randomly selected  and has two strings of 0s   B

number of strings with 1 to s=8

probability of selecting A

P(A)=8/16=1/2

strings in  S starting with S and having two consecutive zeros are 1000,1001

P(AnB)=3/16

the conditional probability that a randomly generated bit string of length four contains at least two consecutive 0s

P(AnB)/P(A)=3/16/1/2

3/8