Question

A box contain 10 green pins 3 are blue and 7 are green. Two pins are randomly taken out of the box without replacement work out the probability that both pins are the same color

Answer 1

Answer:

$P(Z)=\frac{8}{15}$

Step-by-step explanation:

From the question we are told that:

Sample size $n=10$

Green pins $x=7$

Blue pins $y=3$

 

Generally the probability of getting two green is mathematically given by

$P(2X)=\frac{7}{10}*\frac{6}{9}$

$P(2X)=\frac{7}{15}$

Generally the probability of getting two blue is mathematically given by

$P(2Y)=\frac{3}{10}*\frac{2}{9}$

$P(2Y)=\frac{1}{15}$

Therefore the probability that both pins are the same color P(Z)

$P(Z)=P(2Y)+P(2X)\\P(Z)=\frac{7}{15}+\frac{1}{15}$

$P(Z)=\frac{8}{15}$