Question

ALL of the following questions come from this problem: A Jar has 25 Red, 15 Blue, and 10 Green marbles in it. (denoted events R,B,G) Calculate all to the following probabilities:

drawing three marbles all at once. Answer to at least 3 decimals accuracy

1.) Probability none are red?

2.) Expected number of red marbles?

3.) Expected number of green marbles?

Answer 1

Answer)

Probability (p) = favorable/total

Total = 25+15+10 = 50

1)

We need to use binomial formula here

P(r) = ncr*(p^r)*(1-p)^n-r

P(red) = 25/50 = 0.5

ncr = n!/(r!*(n-r)!)

N! = n*n-1*n-2... Till 1

For example 5! = 5*4*3*2*1

Special case, 0! = 1

N = 3 here as we are picking up three marbles

P(none is red)

P(0) = 3c0*(0.5^0)*(1-0.5)^3-0

Required probability is = 0.125

2)

Expected number = n*p

P(red) = 0.5

N = 3

Expected number of red marbles = 0.5*3 = 1.5

3)

P(green) = 10/50 = 0.2

Expected number of green marbles = 0.2*3 = 0.6