Three green balls and two yellow balls are placed in a hat. Two balls are randomly drawn
without replacement. Let X be the number of green balls drawn.
i)X=1
Do you want the probability of drawing 2 green balls?
= (3/5)(2/4) = 3/10
DSFDSA
To find the probability when X = 1 (i.e., one green ball is drawn), we need to calculate the probability of drawing one green ball and one yellow ball.
Step 1: Calculate the total number of ways to draw 2 balls out of 5.
The total number of ways to draw 2 balls out of 5 can be calculated using the combinations formula (nCr).
Here, n is the total number of balls (5), and r is the number of balls drawn (2).
nCr = n! / (r!(n-r)!)
So, the total number of ways to draw 2 balls out of 5 is:
5C2 = 5! / (2!(5-2)!) = 10
Step 2: Calculate the number of ways to draw one green ball and one yellow ball.
Since there are 3 green balls and 2 yellow balls, we can calculate the number of ways to draw 1 green ball and 1 yellow ball using the product rule.
Number of ways to draw 1 green ball = 3C1 = 3
Number of ways to draw 1 yellow ball = 2C1 = 2
Number of ways to draw 1 green ball and 1 yellow ball = 3 * 2 = 6
Step 3: Calculate the probability.
The probability of X = 1 is the number of ways to draw one green ball and one yellow ball divided by the total number of ways to draw 2 balls.
Probability (X=1) = Number of ways to draw 1 green ball and 1 yellow ball / Total number of ways to draw 2 balls
Probability (X=1) = 6 / 10
Therefore, when X = 1 (i.e., one green ball is drawn), the probability is 6/10 or 3/5.
To find the probability that X is equal to 1 (i.e., one green ball is drawn), we need to determine the number of successful outcomes and divide it by the total number of possible outcomes.
Step 1: Determine the number of successful outcomes
To have one green ball and one yellow ball drawn, we have two possibilities: GY (green followed by yellow) or YG (yellow followed by green).
Step 2: Determine the total number of possible outcomes
When drawing two balls without replacement, the total number of possible outcomes is the number of ways to choose any two balls out of the five available. This can be calculated using combinations:
C(5, 2) = 5! / (2! * (5-2)!) = 10
Step 3: Calculate the probability
The probability of X being equal to 1 is the number of successful outcomes divided by the total number of possible outcomes:
P(X=1) = Number of successful outcomes / Total number of possible outcomes
= 2 / 10
= 1/5
= 0.2 or 20%
So, the probability of drawing one green ball without replacement is 0.2 or 20%.