Question

Suppose a jar contains 10 red marbles and 34 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Answer 1

Answer:

The probability that both are red is $P(red\:and \:red)=\frac{45}{946}\approx0.04756\approx4.756\%$.

Step-by-step explanation:

Probability is simply how likely something is to happen and its given by

Probability of an event = (# of ways it can happen) / (total number of outcomes)

Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.

                                     $P(A\:and\: B)=P(A)\cdot P(A|B)$

At our first pull, there is an $P(red)=\frac{10}{10+34}$ chance that a red will be pulled.

At the second pull there is a $P(red)=\frac{9}{9+34}$ chance that the second marble will be red.

Therefore, the probability that both are red is

$P(red\:and \:red)=\frac{10}{10+34}\cdot \frac{9}{9+34}=\frac{45}{946}\approx0.04756\approx4.756\%$