A jar contains 2 orange balls, 5 black balls, and 3 pink balls.

Event A = drawing a black ball on the first draw
Event B = drawing a pink ball on the second draw
If two balls are drawn from the jar, one after the other without replacement, what is P(A and B) expressed in simplest form?

can someone show me a quick, step-by-step on how to do this? thank you! :)

nevermind! i got it. the answer is a.) 1/6.

the choices are:

a.) 1/6
b.) 1/3
c.) 4/9
d.) 5/9

Sure! Here's a step-by-step solution:

Step 1: Find the probability of drawing a black ball on the first draw.
There are a total of 2 + 5 + 3 = 10 balls in the jar. Since there are 5 black balls, the probability of drawing a black ball on the first draw is 5/10, which simplifies to 1/2.

Step 2: Find the probability of drawing a pink ball on the second draw after a black ball was drawn without replacement.
After the first draw, there are now 9 balls remaining in the jar. Since there are 3 pink balls remaining, the probability of drawing a pink ball on the second draw is 3/9, which simplifies to 1/3.

Step 3: Calculate the probability of both events A and B occurring.
To calculate the probability of both event A and B occurring, we need to multiply the probability of event A (drawing a black ball on the first draw) by the probability of event B (drawing a pink ball on the second draw). Therefore:

P(A and B) = P(A) * P(B) = (1/2) * (1/3) = 1/6.

So, the probability of drawing a black ball on the first draw and a pink ball on the second draw without replacement is 1/6.

To find the probability of events A and B occurring, you need to determine the probability of drawing a black ball on the first draw (Event A) and a pink ball on the second draw (Event B) without replacement.

Step 1: Calculate the probability of drawing a black ball on the first draw.
Since there are 10 balls in total, the probability of drawing a black ball on the first draw is 5/10 or 1/2.

Step 2: Calculate the probability of drawing a pink ball on the second draw, given that a black ball was already drawn.
After the first draw, there are now 9 balls remaining in the jar, of which 3 are pink. So, the probability of drawing a pink ball on the second draw after a black ball was drawn is 3/9 or 1/3.

Step 3: Multiply the probabilities of Event A and Event B.
To find the probability of both events occurring, you need to multiply the probabilities calculated in Step 1 and Step 2:

P(A and B) = P(A) * P(B)
= 1/2 * 1/3
= 1/6

So, the probability of drawing a black ball on the first draw and a pink ball on the second draw is 1/6.