I have a question in my math class in college. Here is the question, but I just need help on HOW to answer it. My text isn't clear at all.
A box contains 2 black balls and 3 gold balls. 2 balls are randomly drawn in succession.
a.if there is no replacement, what is the probablity that both balls are black?
b.if there is a replacement before the second draw, what is the probablitity that both balls are black?
My classes are online, and the text is very confusing and the equations for probability all seem to be exactly the same. Please help! Thanks.
a) prob = (2/5)(1/4) = 2/20 = 1/10
b) prob = (2/5)(2/5) = 4/25
So I just multiply the probability of each ball on each turn? Thank you sooo much! Why can't the text just say that?
Sure! I can help you understand how to approach these probability questions.
To answer these questions, we need to understand the concept of probability and the different scenarios involved.
a. Probability without replacement:
When there is no replacement, it means that after drawing one ball, it is not returned to the box before drawing the second ball. In this case, the number of balls in the box decreases by 1 after the first draw.
To find the probability that both balls drawn are black, we need to calculate:
(Number of ways to draw 2 black balls) / (Number of total possible outcomes)
Number of ways to draw 2 black balls: Since there are 2 black balls in the box, we need to select 2 out of 2 black balls. This can be calculated using the combination formula as C(2, 2) = 1.
Number of total possible outcomes: Since there are 5 balls in total (2 black balls + 3 gold balls), we need to select 2 out of 5 balls. This can be calculated as C(5, 2) = 10.
So, the probability of drawing both black balls without replacement is 1/10.
b. Probability with replacement:
When there is replacement, it means that after drawing a ball, it is returned to the box before drawing the next ball. In this case, the number of balls in the box remains the same after each draw.
To find the probability that both balls drawn are black with replacement, we can still use the same formula as in part a:
(Number of ways to draw 2 black balls) / (Number of total possible outcomes)
Number of ways to draw 2 black balls: Since there are 2 black balls in the box, we need to select 2 out of 2 black balls. This can be calculated as C(2, 2) = 1.
Number of total possible outcomes: Since there are 5 balls in total (2 black balls + 3 gold balls), and replacement is allowed, the number of possible outcomes remains the same after each draw. So, we still have C(5, 2) = 10.
Therefore, the probability of drawing both black balls with replacement is still 1/10.
I hope this explanation clarifies the concept of probability and how to approach these types of questions. If you have any further questions, feel free to ask!