Answer to Question #218581 in Statistics and Probability for Tina

Question

4.5 The bag contained three black balls and four orange balls. Thabang picks out a ball, records its colour and then replaces it.
4.5.1 Calculate the probability that the two balls are of the same colour.
4.5.2 Calculate the probability that the two balls are different colours.
4.5.3 Calculate the probability of picking at least one orange ball.

Answer 1

$$3+4=7$$

4.5.1

$$P(2\ same)=P(BB)+P(OO)=\dfrac{3}{7}(\dfrac{3}{7})+\dfrac{4}{7}(\dfrac{4}{7})$$

$$=\dfrac{25}{49}$$

4.5.2

$$P(2\ different)=P(BO)+P(OB)=\dfrac{3}{7}(\dfrac{4}{7})+\dfrac{4}{7}(\dfrac{3}{7})$$

$$=\dfrac{24}{49}$$

4.5.3

$$P(at\ least\ 1\ O)=P(BO)+P(OB)+P(OO)$$

$$=\dfrac{3}{7}(\dfrac{4}{7})+\dfrac{4}{7}(\dfrac{3}{7})+\dfrac{4}{7}(\dfrac{4}{7})$$

$$=\dfrac{40}{49}$$

Or

$$P(at\ least\ 1\ O)=1-P(BB)$$

$$=1-\dfrac{3}{7}(\dfrac{3}{7})$$

$$=\dfrac{40}{49}$$