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Answer 1 · 2017-10-24T10:47:56

$\frac{2}{25}, \frac{9}{100}, \frac{3}{50}$ $2/25, 9/100, 3/50$ respectively

The bag contains in total $4 + 6 + 8 + 2 = 20$ $4 + 6 + 8 + 2 = 20$ marbles.

The probabilities for each colour are as follows:

Blue: $\frac{4}{20} = \frac{1}{5}$ $4/20 = 1/5$

Red: $\frac{6}{20} = \frac{3}{10}$ $6/20 = 3/10$

Green: $\frac{8}{20} = \frac{2}{5}$ $8/20 = 2/5$

Yellow: $\frac{2}{20} = \frac{1}{10}$ $2/20 = 1/10$

For a probability of one thing followed by another, you simply multiply the two probabilities, so

$P (B then G) = \frac{1}{5} \times \frac{2}{5} = \frac{2}{25}$ $P("B then G") = 1/5 xx 2/5 = 2/25$

$P (R then R) = \frac{3}{10} \times \frac{3}{10} = \frac{9}{100}$ $P("R then R") = 3/10 xx 3/10= 9/100$

$P (Y then not G) = ?$ $P("Y then not G") = ?$

This last one is slightly trickier. The probability of something not happening is $1$ $1$ minus the probability that it will happen, or

$P (¯ ¯ ¯ X) = 1 - P (X)$ $P(barX) = 1-P(X)$

therefore

$P (¯ ¯ ¯ G) = 1 - \frac{2}{5} = \frac{3}{5}$ $P(barG) = 1-2/5 = 3/5$

so

$P (Y then not G) = \frac{1}{10} \times \frac{3}{5} = \frac{3}{50}$ $P("Y then not G") = 1/10 xx 3/5 = 3/50$