A fair coin is flipped 12 times in a row. a What is the probability that it lands on tails exactly one third of the times? b What is the probability that it lands on heads at least twice? c What is the probability that the first flip is heads or the last flip is heads?
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- 2. A box contains three fair coins, and two trick coins that have heads on both sides. (a) What is the probability that a randomly selected coin from the box will come up heads when flipped? (b) Suppose you randomly pick a coin from the box and flip it, and it comes up heads. What is the probability that it's one of the trick coins? (c) Let X be the random variable that represents the number of heads when every coin in the box is flipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes, or you can remember that coin flips are independent of each other.) (d) What is the expected number of heads when all the coins are flipped?5. Let X be the random variable that represents the number of hearts in a 4 card hand drawn from a standard deck. (a) What is the probability distribution of X? (b) What is the expected value of X?A math class has 25 students. Assuming that all of the students were born in the first half of the year – between January 1st and June 30th– what is the probability that at least two students have the same birthday? Assume that nobody was born on leap day, so there are 181 possible birthdays.
- cs hw helpThe probability of event A is 55%. The probability of event B is 40%. The probability that A happens given that B has happened is 25%. What is the probability that both A and B happen? 95% 70% 65% 10% 15%Probability and Statistics I have in my pocket ten coins. Nine of them are ordinary coins with equal chances of coming up head and tail when tossed and the tenth has two heads. If I take one of the coins at random from my pocket, what is the probability that it is the coin with two heads ?
- Need the right answer among choices and also an explanation of the answer.algorithmsA box contains three fair coins, and two trick coins that have heads on both sides.(a) What is the probability that a randomly selected coin from the box will come up heads whenflipped? (b) Suppose you randomly pick a coin from the box and flip it, and it comes up heads. What is theprobability that it’s one of the trick coins? (c) Let X be the random variable that represents the number of heads when every coin in the box isflipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes,or you can remember that coin flips are independent of each other.) (d) What is the expected number of heads when all the coins are flipped?Page 2
- When correctly adjusted, a machine that makes widgets operates with a 5% defective rate. However, there is a 10% chance that a disgruntled employee shakes the machine, in which case the defective rate jumps up to 30%. Q41. A coin is flipped four times. Assume all outcomes are equally likely. What is the probability that there are at least two consecutive flips that come up heads? 2. A hand of 5 cards is drawn from a standard deck of 52 cards. Assume all outcomes are equally likely. What is the probability that at least two of the cards have the same rank? Hint: Find the probability of the complement.Q6/ The number of failures for a cryogenics machine from contamination in biological samples is a Poisson random variable with a mean of 0.01 per 100 samples. (a) If the lab usually processes 500 samples per day, what is the expected number of failures per day? (b) What is the probability that the machine will not fail during a study that includes 500 participants? (assume one sample per participant.) Ans. (0.05, 0.9512)