5 balls are picked at random one at a time and then replaced. If 65% of balls are blue, 30% are red and 5% are green. Then what is the probability that
i) All 5 balls are red
ii) 3 are blue, 1 is green and 1 is red
iii) At least 1 is a green
5 balls are picked at random one at a time and then replaced. If 65% of balls are blue, 30% are red and 5% are green. Then what is the probability that
i) All 5 balls are red
ii) 3 are blue, 1 is green and 1 is red
iii) At least 1 is a green
BTW, if the balls were not replaced, then this problem would be unsolvable due to the unknown quantity of balls.
i) $\displaystyle P(red)^5 = 0.3^5$
ii) $\displaystyle P(blue)^3 * P(green) * P(red) = 0.65^3 * 0.3*0.05$
iii) $\displaystyle P(G \ge 1) = 1 - P(ge = 0) = 1 - 0.95^5$
To the OP: Read Multinomial distribution - Wikipedia, the free encyclopedia
The reason it has to be multiplied is exactly because order does not matter.
$\displaystyle
P(blue)^3 * P(green) * P(red) = 0.65^3 * 0.3*0.05
$
Assumes that you first pick three blue balls, then a green one, then a red one. Because order does not matter, you'll need to multiply this by the amount of combinations possible, which in this case is:
$\displaystyle
{\color{red}\frac{5!}{3! \, 1! \, 1!}}$