Math Answers

The Star hotel was burned down in a fire and the manager decided to accommodate the

guests in 4–person and 8-person tents. The tents were to be hired at a cost of Kshs 1,500 and

Kshs 4,500 per night respectively, the space available could accommodate at most 13 tents

and the manager had to cope with at least 64 guests.

Required

Formulate this as a linear programming model that could be used to determine the number

of tents of each type that could pull up in order to minimize the overall cost. (10 Marks

5. What is the probability that exactly eight 0 bits are generated when 10 bits are generated with the probability that a 0 bit generated is 0.9, the probability that a 1 bit generated is 0.1, and the bits are generated independently?

4. An unbiased coin is tossed twice. If A is the event: both head or tail have occurred and B is the event: at most one tail is observed find : i) P(A) ii) P(B) iii) P(A\B) iv) P(B\A)

3. A box contains 4 bad and 6 good tubes. Two are drawn out from the box at a time. One is tested and found to be good. What is the probability that the other one is also good?

2. A random experiment has m outcomes a₁,a₂....,a_m and another has out out comes b₁,b₂.......,b_n. Describe the sample space when both the experiment carried out.

1. A coin is tossed twice. If the second throw results in tail a die is thrown.

Describe the sample space for this experiment.

Find an equation of the ellipse having a major axis of length 10 and foci at , (1,−2 )and , (−7,−2.)

Show that the explicit sequence {yn}∞n=0 such that yn = A(2n )+ B(-1)n for any nonzero

constants A and B is the solution of the recurrence relation

yn = yn-1 + 2yn-2 for n >1.

Permutation and Combination:

1. In how many ways can 7 students be selected in a row of 7 seats if 2 of the students insist of sitting beside each other?
2. In a gathering, the host make sure that each guest shakes hands with everyone else. If there are 30 guest how many handshakes will done?

How many possible samples of size n=8 can be drawn from a population of size 11