Suppose that a coin with probability 0.7 of heads is tossed 100 times. Let X be the number of heads obtained.
What is the probability of obtaining a streak of at least 15 consecutive heads in the 100 tosses?
Suppose that a coin with probability 0.7 of heads is tossed 100 times. Let X be...
A fair coin is tossed 20 times. Let X be the number of heads thrown in the first 10 tosses, and let Y be the number of heads tossed in the last 10 tosses. Find the conditional probability that X = 6, given that X + Y = 10.
A fair coin is tossed 20 times. Let X be the number of heads thrown in the first 10 tosses, and let Y be the number of heads tossed in the last 10 tosses. Find the conditional probability that X = 6, given that X + Y = 10.
a. Suppose that a fair coin is tossed 15 times. If 10 heads are observed, determine an expression / equation for the probability that 7 heads occurred in the first 9 tosses. b. Now, generalize your result from part a. Now suppose that a fair coin is to be tossed n times. If x heads are observed in the n tosses, derive an expression for the probability that there were y heads observed in the first m tosses. Note the...
Suppose that a coin is tossed three times. We assume that a coin is fair, so that the heads and tails are equally likely. Probability that two heads are obtained in three tosses given that at least one head is obtained in three tosses is ___________ Probability that that one head is obtained in three tosses given that at most one head is obtained in three tosses is ____________ at least one means one or more, at most one means...
7.) Suppose that a fair coin is tossed 10 times and lands on heads exactly 2 times. Assuming that the tosses are independent, show that the conditional probability that the first toss landed on heads is 0.2. 8.) Suppose that X is uniformly distributed on [0,1] and let A be the event that X є 10,05) and let B be the event that X e [0.25,0.5) U[0.75,1.0). Show that A and B are independent.
A fair coin is tossed three times. Let X be the number of heads that come up. Find the probability distribution of X X 0 1 2 3 P(X) 1/8 3/8 3/8 1/8 Find the probability of at least one head Find the standard deviation σx
A coin is tossed, what is the probability that two consecutive heads or two consecutive tails occur in at most four tosses? Draw a tree diagram first.
1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? [5] c. Compute P(A), P(B), P(A|B), and P(B|A). [7]
1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? [5] c. Compute P(A), P(B), P(A|B), and P(B|A). [7]
A biased coin is tossed n times. The probability of heads is p and the probability of tails is q and p=2q. Choose all correct statements. This is an example of a Bernoulli trial n-n-1-1-(k-1) p'q =np(p + q)n-1 = np f n- 150, then EX), the expected value of X, is 100 where X is the number of heads in n coin tosses. f the function X is defined to be the number of heads in n coin tosses,...