a gumball machine contains orange yellow and purple gumballs the probability of getting an orange gumball is 3/4 the probability of getting a yellow gumball is 1/6 if there are 36 gumballs in the machine how many are purple?
prob(yellow) = 1/6= x/36, so x = 6 , 6 yellows
prob(orange) = 3/4 = y/36, so y = 27, 27 orange
remaining 3 must be orange
or
1/6 + 3/4 = 11/12
leaving 1/12 for the purple
(1/12)(36) = 3 purple
Let's first find the probability of getting a purple gumball.
The probability of getting a purple gumball can be found by subtracting the sum of the probabilities of getting an orange and a yellow gumball from 1 (since the total probability of getting any color gumball should be 1).
The probability of getting an orange gumball is 3/4, and the probability of getting a yellow gumball is 1/6.
So, the probability of getting a purple gumball can be calculated as:
1 - (3/4 + 1/6)
Next, we need to find the number of purple gumballs in the machine.
Let's assume there are p purple gumballs.
Now, we can set up an equation:
(3/4 + 1/6) * 36 = p
Simplifying the equation:
(18/24 + 4/24) * 36 = p
(22/24) * 36 = p
(11/12) * 36 = p
33 = p
Therefore, there are 33 purple gumballs in the machine.
To determine the number of purple gumballs, we need to find the proportion of purple gumballs out of the total number of gumballs in the machine.
Let's start by finding the total probability of getting an orange or yellow gumball. According to the given information, the probability of getting an orange gumball is 3/4, and the probability of getting a yellow gumball is 1/6.
Therefore, the combined probability of getting either an orange or yellow gumball is:
P(orange) + P(yellow) = 3/4 + 1/6
To add these fractions, we need a common denominator:
(3/4) + (1/6) = (18/24) + (4/24) = 22/24
The remaining probability is for purple gumballs:
P(purple) = 1 - P(orange or yellow)
P(purple) = 1 - 22/24
To simplify this fraction further, we can express 1 as 24/24:
P(purple) = 24/24 - 22/24
P(purple) = 2/24
Now we know that 2/24 of the total gumballs are purple. To find how many gumballs in the machine are purple, we can set up a proportion:
(2/24) = x/36
Solving for x (the number of purple gumballs):
2 * 36 = 24 * x
72 = 24x
x = 72/24
x = 3
Therefore, there are 3 purple gumballs in the machine.