Question

A biased die is thrown 30 times and number of sixes seen is 8. If the die is thrown a further 12 times .
Find,
A) the probability that a 6 will exactly twice.
B) the expected number of sixes.
C) the variance of the number of sixes.

Answer 1

Answer:

External length (l) of bookshelf=85㎝

External breadth (b) of bookshelf=25㎝

External height (h) of bookshelf=110㎝

External surface area of book shelf while leaving out the front face of the shelf=lh+2(lb+bh)

=(85×110)+2(85×25+25×110)

=9350+9750

=19100㎠

Area if front face=(85×110)−75×100+2(75×5)

=1850+760=2600㎠

Area to be polished=19100+2600=21700㎠

Cost of polishing=Rs. 21700×0.20=Rs.4340

Length, breadth and height of each row of bookshelf are

75㎝,20㎝ & 30㎝ respectively. From the figure Area to be painted in 1 row=2(l+h)b+lh

=2(75+30)20+75×30

=6450㎠

Area to be painted in 3 rows=3×6450=19350㎠

Total cost of painting=Rs.(19350×0.1)=Rs. 1935

Total expenses=Rs.(4340+1935)=Rs. 6275

Answer 2

Answer:

A) Probability that a 6 will appear exactly twice is 0.211

B) Expectation of the number of sixes is 3.2

C) Variance of the number of sixes is 2.347

Step-by-step explanation:

A)

Let p be the probability that a six will appear then p = 8/30 which is equal to 4/15

Now that the probability that six will not appear p' = 11/15.

We can the distribution as Binary. Let X be the no.of sixes will appear then

                             X ~B(n,p)

Where n is no.of throws.

Now P(X=2) = $12C_{2} ((4/15)^{2} )((11/15)^{10} )$ which will give 0.211.

B) Expectation, E(x) = np = 12x4/15 = 3.2

C)Variance, V(x)=npq = 12x4/15x11/15 = 2.347.