Question

sionsSuppose a jar contains 13 red marbles and 24 blue marbles. If you reach in the jar and pull out 2 marbles atrandom at the same time, find the probability that both are red.

Answer 1

Given data:

13 red marbles

24 blue marbles

Total marbles:37

probability that both are red P(r,r)

`\begin{gathered} P(r,r)=P(r_1)\cdot P(r_2) \\ \\ P(r_1)=\frac{\#red\text{ marbles}}{\#total\text{ marbles}}=(13)/(37) \\ \\ IntheP(r_2)\text{ the number of red marbles is one less the initial (as the frist marble } \\ \text{is red }and\text{ it is outside the jar)} \\ \\ P(r_2)=\frac{#red\text{ marbles}}{#total\text{ marbles}}=(12)/(37) \\ \\ \\ \\ P(r,r)=(13)/(37)\cdot(12)/(37)=(156)/(1369)=0.114 \end{gathered}`Then, the probability of pull out 2 red marbles is 0.114 (11.4%)