Question

In a game, a participant pays Rs. 20 to roll a dice. If he gets a prime number, he wins Rs. 30; if he gets a composite number, he loses his money; and if he gets neither prime nor composite, he gets Rs. 50. What is his average profit percentage?

Answer 1

@queelius

Answer 2

prime-2,3,5 so 1/2-->30

Answer 3

composite 4,6 so 1/3 --> lose -20

Answer 4

gets neither prime nor composite so 1 --1/6--->rs50

Answer 5

30/2-20/38+50/6=16.66

Answer 6

@kropot72

Answer 7

@ganeshie8

Answer 8

@dg2
The integers between 1 and six may be sorted into these three sets.

Prime: {2, 3, 5}, three in number
Composite: {4, 6}, two in number
Neither: {1}, one in number

P(prime) = 3/6 = 1/2
P(composite) = 2/6 = 1/3
P(neither) = 1/6

This is the expectation of the profit.

E[profit]
= (1/2)(30 - 20) + (1/3)(-20) + (1/6)(50 - 20)
= 5 - 20/3 + 5
= 10/3

The expectation of the profit is Rs. 10/3. For the expectation of the profit percentage that must be divided by the investment.

(10/3)/20 = 1/6 = (100/6)% ≈ 16.7%
Hope it helps