Question

a bag contains 5 red skittles, 3 purple skittles, and 2 orange skittles.A skittle is removed and not replaced, then another skittles.A is removed.what is the probability that is a red skittle then a orange skittle?

Answer 1

The probability of two independant events $P_a$ and $P_b$ can be found by multiplying the individual probabilities like so:
$P_t=P_{a}*P_b$

For each individual probability we can find the answer via a simplfied representation: 
$P_x = \frac{wanted}{total}$

For the first skittle (red) we have:
$P_{red} = \frac{red}{total}=\frac{5}{10}=0.5$

For the second skittle (orange) we have:
$P_{orange} = \frac{2}{9} = 0.2222...$
**(Notice that the total is now NINE since we didn't put the first red one back in the bag.)

So:
$P_{total} = P_{red} \times P_{orange}$
$P_{total} = \frac{5}{10} \times \frac{2}{9}$
$P_{total} = \frac{10}{90}=\frac{1}{9} \approx 0.1111 \approx 11.11\%$