A box contains 10 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 colour.
Must show working

The probability is 8/15

Step-by-step explanation:

Firstly, we identify the probabilities of picking each of the colors as follows;

The probability of picking a blue pin P(b) is 3/10 while the probability of picking a green pin P(g) is 7/10

Now to pick  pins of the same colors after two attempts mean we either pick P(g).P(g) or P(b).P(b)

We must know that the balls are picked without replacement. Picking without replacement mean when the ball is picked, it is removed from the mix and will not be replaced when making another selection

The probability of picking two greens one after the other without replacement = 7/10 × 6/9 = 42/90 = 7/15

The probability of picking two blue pins one after the other without replacement is 3/10 × 2/9 = 6/90 = 1/15

In probability, once we have 'or' we add;

Hence P(g).P(g) or P(b).P(b) = 7/15 + 1/15 = 8/15