Probability is the # of possible outcomes desired / # of possible total outcomes. In problems like this when you have consecutive draws, you find the probability of each individual draw and then multiply your results.
a. there are 4 reds to possible draw from the urn, there are 11 total marbles. The probability of drawing 1 red is 4/11.
After the 4/11 chance that you did get a red, now what is the probability of getting a second red?
*Note, the was no replacing so you have 1 red in your hand and 3 in the urn.
Now there is a 3/10 probability of getting the second red marble. 10 because you have one of the 11 in your hand so there are only 10 left in the urn.
so we have 4/11 and 3/10, multiply and we get 12/110 which reduces to 6 /55
b. same idea just keep your colors and number of marbles straight.
P(red) = 4/11
P(b after a red has been drawn) = 2/10, 2 blue still in the urn but only 10 marbles since you have 1 red in your hand.
Multiply 4/11 and 2/10 which equals 8/110 = 4/55
c. P(b) = 2/11, P(red after a blue has been drawn) = 4/10, multiply 8/110 = 4/55
d. this one is different, you have to account for either one being red or blue. so a red then blur or a blue then a red. We have already found these probabilities in b. and c. Since both situations need to be counted then we add them together. 4/55 +4/55 = 8/55
Why don't we multiply? Because that would give us a smaller probability and if you think about the problem, out chances increase if the order doesn't matter. (yes there is a mathematical explanation but I like to use common sense when possible)