91影视

What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up heads?

Use the law of total expectation to find the average weight of a breeding elephant seal, given that 12% of the breeding elephant seals are male and the rest are female, and the expected weights of a breeding elephant seal is 4200 pounds for a male and 1100 pounds for a female.

What is the probability that a positive integer not exceeding 100 selected at random is divisible by 5 or 7\(?\)

Find the probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive inte- gers not exceeding $$\begin{array}{llll}{\text { a) } 30 .} & {\text { b) } 36 .} & {\text { c) } 42 .} & {\text { d) } 48}\end{array}$$

Let \(A\) be an event. Then \(I_{A}\) , the indicator random variable of \(A\) , equals 1 if \(A\) occurs and equals 0 otherwise. Show that the expectation of the indicator random variable of \(A\) equals the probability of \(A,\) that is, \(E\left(I_{A}\right)=p(A)\)

A run is a maximal sequence of successes in a sequence of Bernoulli trials. For example, in the sequence \(S, S, S, F, S, S, F, F, S,\) where \(S\) represents success and \(F\) represents failure, there are three runs consisting of three successes, two successes, and one success, respectively. Let \(R\) denote the random variable on the set of sequences of \(n\) independent Bernoulli trials that counts the number of runs in this sequence. Find \(E(R) .[\text { Hint: Show }\) that \(R=\sum_{j=1}^{n} I_{j},\) where \(I_{j}=1\) if a run begins at the \(j\) th Bernoulli trial and \(I_{j}=0\) otherwise. Find \(E\left(I_{1}\right)\) and then find \(E\left(I_{j}\right),\) where \(1

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 the probabilities of a 0 and a 1 are the same.)

Assume that the probability a child is a boy is 0.51 and that the sexes of children born into a family are independent. What is the probability that a family of five children has a) exactly three boys? b) at least one boy? c) at least one girl? d) all children of the same sex?

A group of six people play the game of 鈥渙dd person out鈥� to determine who will buy refreshments. Each person flips a fair coin. If there is a person whose outcome is not the same as that of any other member of the group, this person has to buy the refreshments. What is the probability that there is an odd person out after the coins are flipped once?

Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if a) a 0 bit and a 1 bit are equally likely. b) the probability that a bit is a 1 is 0.6 . c) the probability that the ith bit is a 1 is 1\(/ 2^{i}\) for \(i=\) \(\quad 1,2,3, \ldots, 10\)