Question

Twenty bags of marbles are sitting on a table. In each of the bags 80% of themarbles are red. If you randomly selectone marble from each bag, what is theprobability of getting exactly fourteenred ones?

Answer 1

0.11

Explanation

Given that the selecting marbles are or are not red, then we can model this situation with the binomial distribution. Binomial probability, P(x), is calculated as follows:

`P(x)=C(n,x)\cdot p^x(1-p)^(n-x)`

where

• n: number of trials

,

• x: number of times for a specific outcome within n trials

,

• C(n, x): number of combinations

,

• p: probability of success on a single trial, as a decimal

In this case, we have n = 20 trials (total number of bags), the number of successes is x = 14 (number of bags at which a red marble is selected), the probability of success is p = 0.8 (probability of picking a red marble in each bag). Substituting these values into the formula, we get:

`\begin{gathered} P(14)=C(20,14)\cdot0.8^(14)\cdot(1-0.8)^(20-14) \\ P(14)=38760\cdot0.8^(14)\cdot0.2^6 \\ P(14)\approx0.11 \end{gathered}`