1 playing a certain game on each play you have a 40 chance o

1- playing a certain game on each play you have a 40% chance of winning , let x=the number of trials until three successes. whats the probability that you will have your third success on the third trial?

2- you roll a die until obtaining three 1s what s the probability of rolling the die at least six times?

3- draw five card without replacement let x = the number of reds. find the expected value and variance of x.(hint: how many red cards in the deck? how many total cards?)

4- a website on average gets 15 hits daily, what is the probability there will be no hit in the next hour?

5- Suppose that the probability that a person books an airline ticket using an online travel website is 0.68. For the questions that follow, consider a sample of fifteen randomly selected people who recently booked an airline ticket.

A-What is the probability that no more than four out of fteen people used an online travel website when they booked their airline ticket? Round to the nearest thousandth

B- Out of fteen randomly selected people, how many would you expect to use an online travel website to book their airline ticket, give or take how many? Round to the nearest whole person.

Solution

5) P = 0.68

N = 15

A) PROBABILITY NOT MORE THAN 4 = P(0)+P(1)+P(2)+P(3)+P(4)

= 15C0(0.68)^0*(0.32)^15 + 15C1*(0.68)^1*(0.32)^14+15C2*(0.68)^2*(0.32)^13+15C3*(0.68)^3*(0.32)^12 +15C4*(0.68)^4*(0.32)^11 = 0.008

B)N = 15

EXPECTATION = 15*0.68 = 10.2 = 10