A golf bag contains 6 white balls and 8 yellow balls. What is the probability of each event?
A) Drawing 3 white balls?
B.) Drawing 1 Yellow ball and 1 white ball?
Thanks
in A, are you drawing only 3 balls?
then prob = (6/14)(5/13)4/12) = 5/91
or C(6,3)/C(14,3) = 20/364 = 5/91
in B, are you drawing only 2 balls?
then (8/14)(7/13) = 4/13
or C(8,2)/C(14,2) = 28/91 = 4/13
binomial distribution
p white = 6/14 = 3/7
p yellow = 1 - pwhite = 4/7
in three trials, what is the chance of drawing exactly 3 white?
The binomial coef of 3 out of three is 1
because 3!/(3!(3-3)!) = 1
P(3/3) = 1 * (3/7)^3 * (4/7)^0
so (3/7)^3
What is the probability of drawing exactly one white out of 2 trials?
C(2/1) = 2!/[1! (2-1)!] = 2
P(1/2) = 2 * (3/7)^1 * (4/7)^1
= 24/49
Use what Reiny wrote. I ignored the changes in probability as the bag contained fewer balls.
To find the probability of each event, we need to determine the total number of possible outcomes and the number of favorable outcomes for each event.
Let's start with event A) Drawing 3 white balls:
1. Total number of possible outcomes: Since there are 14 balls in total in the golf bag, the number of total possible outcomes is C(14, 3), which represents the number of ways to choose 3 balls out of 14.
2. Number of favorable outcomes: Since there are 6 white balls in the golf bag, the number of ways to choose 3 white balls out of the 6 is C(6, 3).
The probability of event A is then the number of favorable outcomes divided by the total number of possible outcomes:
P(A) = C(6, 3) / C(14, 3)
For event B) Drawing 1 Yellow ball and 1 white ball:
1. Total number of possible outcomes: Since there are 14 balls in total in the golf bag, the number of total possible outcomes is C(14, 2), which represents the number of ways to choose 2 balls out of 14.
2. Number of favorable outcomes: We need to consider the cases where we choose 1 yellow ball out of 8 and 1 white ball out of 6. Therefore, the number of favorable outcomes is C(8, 1) * C(6, 1).
The probability of event B is then the number of favorable outcomes divided by the total number of possible outcomes:
P(B) = (C(8, 1) * C(6, 1)) / C(14, 2)
By calculating the combinations using factorials and performing the division, we can find the exact probabilities for events A and B.