ANSWERS ARE AT THE BOTTOM.
To find the probability of 2 events happening in a row, we need to multiply their probabilities.
For example, if a friend bet: "If you roll a six on a dice and filp and coin and get heads, then I'll give you 500 bucks. However, if you don't roll a six and flip and coin and get heads in a row, then you have to give me 500 bucks."
You want to know the probability of you winning this bet.
So, we need to multiply the probability of rolling a six, and the probability of flipping a coin and landing heads.
This is 1/6 * 1/2
That is 1/12
You probably should't take this bet, because you only have a 1/12 chance of winning.
Lets go back to your problem. The jar contains 16 red marbles and 28 blue marbles. The probability of picking a red marble right now is 16/28, or 4/7. Assume we picked a red marble on our first try. Now, there are only 15 red marbles. The probability of picking a red marble right now is 15/28.
Probability of picking a red marble on your first try: 4/7
Probability of picking a red marble on your second try: 15/28
Now, we need to multiply the probabilities.
4/7 * 15/28
60/196
15/49
ANSWER:
15/49
