I need some help with the set up please.
Joella has a bag of marbles. The bag contains 10 red marbles, 5 green marbles, and 3 blue marbles. She will randomly select 2 marbles from the bag one at a time without replacement. What is the probability that Joella will select a red marble first and then a blue marble?
I got 10/18*3/16, but when I solve it, the answer is not one of the multiple choice answers. Thank you.
try 10/18*3/17
how about 10/18 * 3/17 ??
To solve this problem, we can use the concept of probability. The probability of an event is defined as the number of favorable outcomes over the total number of possible outcomes.
In this case, Joella's bag contains a total of 10 + 5 + 3 = 18 marbles. Since Joella is selecting marbles without replacement, after selecting one marble, there will be one less marble in the bag. Therefore, the total number of possible outcomes for the first selection is 18.
To find the probability of selecting a red marble first, we need to determine the number of favorable outcomes. Joella has 10 red marbles in the bag, so for the first selection, there are 10 red marbles out of the total 18 marbles.
After selecting a red marble, there will now be 9 red marbles left in the bag, out of a total of 17 marbles remaining. For the second selection, Joella wants to select a blue marble. She has 3 blue marbles left in the bag, so the number of favorable outcomes for the second selection is 3.
Therefore, the probability of Joella selecting a red marble first and then a blue marble can be calculated as:
P(Red first then Blue) = (Number of favorable outcomes) / (Total number of possible outcomes)
= (10/18) * (3/17)
Simplifying this expression, we get:
P(Red first then Blue) = 30/306
= 5/51
So the correct answer to the probability is 5/51, not 10/18 * 3/16.