Question

A bag had 7 orange rocks , 6 green rock , 1 white rock ,7 black rocks , and 2 yellow you randomly pull a rock from the bag ,keep it out , and then pull out another one .
What is the probability of getting a yellow rock and then a n orange rock ?

Answer 1

Answer:

$Probability = \frac{7}{253}$

Step-by-step explanation:

Given

$Orange = 7$

$Green = 6$

$White = 1$

$Black = 7$

$Yellow = 2$

Required

Probability of selecting a yellow then orange rock

From the question, we understand that the probability is that of without replacement.

Since the yellow, is first picked.

We need to determine the probability of picking a yellow rock, first.

$P(Yellow) = \frac{n(Yellow)}{Total}$

$P(Yellow) = \frac{2}{7 + 6 + 1 + 7 + 2}$

$P(Yellow) = \frac{2}{23}$

The rock has reduced by 1;

Next is to determine the probability of picking an orange rock

$P(Orange) = \frac{n(Orange)}{Total - 1}$

$P(Orange) = \frac{7}{7 + 6 + 1 + 7 + 2- 1}$

$P(Orange) = \frac{7}{22}$

The required probability is calculated as thus:

$Probability = P(Yellow) * P(Orange)$

$Probability = \frac{2}{23} * \frac{7}{22}$

$Probability = \frac{14}{506}$

$Probability = \frac{7}{253}$