5)P(land on head at least twice) =P(from Jar 1 and land on heads at least twice)+P(from Jar 2 and land on heads at least twice)
=(1/2)*(3C2(2/3)2(1/3)+3C3(2/3)3(1/3)0)+(1/2)*(3C2(1/3)2(2/3)+3C3(1/3)3(2/3)0)=0.5
6)
we assume that consecutive tests are independent
P(infected given tested positive twice) =P(infected and tested positive twice)/P(tested positive twice)
=(0.0001*0.995*0.995)/(0.0001*0.995*0.995+0.9999*0.001*0.001)=0.9900
5.) A jar contains 50 type 1 coins and 50 type 2 coins. Type 1 coins...
A jar contains 100 coins, where 99 are fair, but one is double-headed (always landing heads). A coin is chosen randomly from the jar. Then, the chosen coin is flipped 5 times. (a) Compute the probability that the coin lands heads all 5 times. (b) Given the coin lands heads all 5 times, what is the probability that the chosen coin is double-headed?
6. A bag has 3 type A coins and 2 type B coins. The probability of heads with a type A coin is 1/4 and that with a type B coin is 1/2. A coin is randomly chosen from the bag and tossed. Given that the coin lands heads, what is the probability that it is of type A?
1. A jar has two kinds of coins. Some of them are fair, and some of them have are biased, in which case P(heads) = 2 . 3 A coin is selected from the jar. Since we don’t know which kind it is, we toss it 50 times. Let X be the number of heads that occur. Please note carefully the directions of the inequalities (≤ or ≥) in each of the questions below. (a) Suppose the coin chosen is...
there are two coins. One is fair and the other one has a 5/8 probability to heads. A coin is chosen at random and tossed twice. Heads shows twice. What is the probability the coin you chose is the biased one
Consider a coin with probability q of landing on heads, and probability 1−q of landing on tails. a) The coin is tossed N times. What is the probability that the coin lands k times on heads. b) The coin is tossed 100 times, and lands on heads 70 times. What is the maximum likelihood estimate for q?
6. Jar of Coins. 100 quarters. Most of Coins. Note: Thiadaned from a Google interview question. I have a jar Most of them are ar fi luarters, but 12 of them are takel of these fala eads on both sides and 5 have tails on both sides. quarters, 7 have heads on both sides and 5 have a) If you select a coin from the cct a coin from the jar at random and flip it 3 times and get...
You have 2 fair coins and one coin with heads on both sides. You pick a coin at random and toss it twice. If it lands heads up on both tosses, the probability it also lands heads up on a third toss can be express in the form A/B, where A and B are relatively prime positive integers (i.e. the greatest common divisor is 1). Compute A + B.
A box contains five coins. For each coin there is a different probability that a head will be obtained when the coin is tossed. (Some of the coins are not fair coins!) Let pi denote the probability of a head when the i th coin is tossed (i = 1, . . . , 5), and suppose that p1 = 0, p2 =1/4, p3 =1/2, p4 =3/4, p5 =1. The experiment we are interested in consists in selecting at random...
The probability of getting 2 heads and 1 tail when three coins are tossed is 3 in 8. Find the odds of not getting 2 heads and 1 tail. ANSWER: 5:8?Three Coins are tossed. Find the probability that exactly 2 coins show heads if the first coin shows heads.?ANSWERS: Could it be 1/4?
when coin 2 is flipped it lands on heads with When coin 1 is flipped, it lands on heads with probability probability (a) If coin 1 is flipped 12 times, find the probability that it lands on heads at least 10 times. (b) If one of the coins is randomly selected and flipped 9 times, what is the probability that it lands on heads exactly 6 times? (c) In part (b), given that the first of these 9 flips lands...