The number of chain links required to pay for n days.

a traveler owing a gold chain with 7 links is accepted at an inn on condition that he pay one link of the chain for each day he stays. if the traveler is to pay daily and may be given links already used in payment as change, show that he only needs to take out one of the links of the chain in order to pay each day for 7 days. (n ...continues

Null & Alternative Hypotheses : T-Tests

Ten people agree to take part in an experiment designed to determine whether a persons weight differs between morning & evening. Each person is weighed last thing at night & first thing in the morning, wearing the same clothes. The results, giving weights in kilogrammes are below. weight 1 2 3 4 5 6 7 8 ...continues

Data Analysis : Null Hypotheses and Normal Distribution

A random sample of 8 petrol stations in each of three European countries A, B and C was taken. The price per litre at each station was recorded in Euros. The prices are given below. A 7.80 8.00 7.98 8.20 8.00 7.99 8.10 7.90 B 8.01 7.75 8.00 7.77 8.01 8.01 8.12 8.20 C 8.10 7.92 8.01 7.88 8.30 8.22 8.56 8.10 Discuss wa ...continues

Probability based on Random Selection

A student taking a multiple choice examination does not know the answer to two questions. All have five choices for the answer. For one of the two questions the student can eliminate two answer choices as incorrect but has no idea about the other answer choices for that question. For the other question, the student has no clu ...continues

Probability Based on Order and Random Selection

Four couples, each consisting of one man and one woman, are seated at a circular table. Assuming that each different order is equally likely, find the probability that: a) Andrew is sitting next to his partner b) Benjamin, Charles and David are sitting together (in any order) c) The men and women sit alternately

Probability : Fair and Biased Coins

A hat contains n coins, f of which are fair and b of which are biased to land on heads with a probability of 2/3. A coin is drawn from the hat and tossed twice. The first time it lands heads and the second time it lands tails. Given this information, what is the probability that a fair coin has been chosen?

Probability of Picking Groups of Cards

Find the probability that a hand of 13 cards dealt from a well shuffled pack of 52 contains: a) Exactly two kings and one ace b) Exxactly one ace given that it contains exactly two kings c) Exactly 10 spades d) At least two diamonds given that it contains exactly 3 spades and 4 hearts.

Probability Based on Random Selection

There are three boxes, each with two drawers. Box I has a gold coin in each drawer Box II has a silver coin in each drawer Box III has a gold coin in one drawer and a silver coin in the other. One box is chosen at random and a drawer is opened from that box. If it contains a gold coin, find the probability that it is in ...continues

Probability

Show that the probability that exactly one of the events A and B occurs is (see attached).

Probability

FULL WORKINGS PLEASE. Clair and Helen frequently play each other in a series of games of table tennis. Records of the outcomes of these games show that whenever they play a series of games, Clair has a probability 0.6 of winning the first game and that in every subsequent game in the series, Clair's probability of winning the ...continues