another probability question?

Question

ok so to this problem:

I got the probability question..i got to chose one of m&m's bags and find the probability of each color in the bag,showing the data in a ratio and percent,
so in the bad i chose is 59 m&m's
red are 9
orange are 21
blues are 9
browns are 5
yellows are 9
and greens are 6

NOW I NEED TO FIND THE PROBABILITY OF PICKING ONE YELLOW OUT OF THE BAG,REPLACING IT AND PICK AN ORANGE..


HELP MEEEEEEE PLEASEEEE

Answer 1

By definition probability is P(s) = n(s)/N; where n(s) is the number of outcomes to succeed and N is the total number of outcomes, which include both success and failure (f).

Suppose you designate drawing a yellow M&M as a success. In math talk s = yellow; so P(s = yellow) = n(s = yellow)/N. If you draw an M&M from your bag of 59 M&M's, there are n(s = yellow) = 9 ways to succeed. And each M&M in the bag is a possible outcome, both success and failure outcomes; so N = 59 possible outcomes.

Thus, from the definition P(s = yellow) = n(s = yellow)/N = 9/59, which is the probability of selecting a yellow M&M from the bag of N = 59 M&M's. Similarly, we replace the M&M after the first draw; so N is still 59 M&M's. But this time n(s = orange) = 21; so P(s = orange) = n(s = orange)/N = 21/59.

Your plea: NOW I NEED TO FIND THE PROBABILITY OF PICKING ONE YELLOW OUT OF THE BAG,REPLACING IT AND PICK AN ORANGE can unfortunately be interpreted two ways. If you are asking what is the probability for drawing a yellow and then, after replacement, what is the probability for drawing an orange, each of those is the probability already found above (i.e., 9/59 and 21/59), you can solve for the two percents.

However, if you are asking what is the joint probability of drawing the yellow and the orange, with replacement, that is the multiple of the two probabilities found earlier. P(yellow AND orange) = P(yellow)P(orange) when the two draws are independent, which they are with replacement. You can do the math as both ratios and percentages.

Answer 2

Probability of picking a yellow is 9/59. If you replace it, the probability of picking an orange is 21/59. So the probability of picking a yellow, replacing it and subsequently picking an orange is (9/59)*(21/59).