Question

1. A basket contains 12 black marbles, 14 red marbles and 12 green marbles. What is the probability of picking a black marble first and then a red marble with replacement?
2. A box has 3 netball and 6 volleyball cards. What is the probability of selecting...
A, a netball card, keeping it out, and then selecting another netball card?
B, a netball card, keeping it out, and then selecting a volleyball card?

Answer 1

1. Total number of marbles = 12+14+12=38

The probability of selecting black marble is

$P(black) = \frac{12}{38} = \frac{6}{19}$

Since the marble is replaced, so total number of marbles will remain same.

So, the probability of selecting red marble is

$P(red) = \frac{14}{38} = \frac{7}{19}$

Therefore, the probability of selecting a black marble first and then a red marble with replacement is calculated as follows:

$P(black, \; then \; red) = P(black) \times P(red) \\ = \frac{6}{19} \times \frac{7}{19} \\ = \frac{42}{361}$

2. Total number of cards = 3 +6 =9

A) $P= \frac{3}{9} \times \frac{2}{8} = \frac{6}{72} = \frac{1}{12}$

B) $P = \frac{3}{9} \times \frac{6}{8} = \frac{18}{72}=\frac{1}{4}$