Kayla has a bag of M&Ms. Her bag has red, blue, yellow, brown, green, and orange M&Ms
Kayla has a bag of M&Ms. Her bag has red, blue, yellow, brown, green, and orange M&Ms. If she picks a candy without looking:
The probability of picking a red M&M is one fourth.
Red and orange have an equal probability of being picked.
The probability of picking a brown M&M is half the probability of picking a red M&M.
Brown and yellow have an equal probability of being picked.
Blue and green have an equal probability of being picked.
If Kayla had 24 M&Ms, how many would be:
Yellow?
Brown?
Green ?
The Correct Answer and Explanation is :
To determine the number of yellow, brown, and green M&Ms in Kayla’s bag of 24 M&Ms, we can use the provided probabilities and the total number of M&Ms.
Given Probabilities:
- Red M&Ms: Probability = 1/4
- Red and Orange M&Ms: Equal probability
- Brown M&Ms: Probability = 1/8 (half of red M&Ms)
- Brown and Yellow M&Ms: Equal probability
- Blue and Green M&Ms: Equal probability
Step 1: Assign Variables
Let the probabilities of each color be represented as follows:
- Red M&Ms: P(R) = 1/4
- Orange M&Ms: P(O) = 1/4
- Brown M&Ms: P(B) = 1/8
- Yellow M&Ms: P(Y) = 1/8
- Blue M&Ms: P(Bl) = x
- Green M&Ms: P(G) = x
Step 2: Set Up the Equation
The total probability must sum to 1:
P(R) + P(O) + P(B) + P(Y) + P(Bl) + P(G) = 1
Substitute the known values:
1/4 + 1/4 + 1/8 + 1/8 + x + x = 1
Step 3: Solve for x
Combine like terms:
1/2 + 1/4 + 2x = 1
1/4 + 2x = 1/2
2x = 1/4
x = 1/8
Step 4: Calculate the Number of M&Ms
Now, calculate the number of M&Ms for each color:
- Red M&Ms: (1/4) × 24 = 6
- Orange M&Ms: (1/4) × 24 = 6
- Brown M&Ms: (1/8) × 24 = 3
- Yellow M&Ms: (1/8) × 24 = 3
- Blue M&Ms: (1/8) × 24 = 3
- Green M&Ms: (1/8) × 24 = 3
Conclusion:
- Yellow M&Ms: 3
- Brown M&Ms: 3
- Green M&Ms: 3
Explanation:
The problem provides specific probabilities for each color of M&M in Kayla’s bag. By assigning variables to the unknown probabilities and using the fact that the total probability must sum to 1, we can set up an equation to solve for the unknown probabilities. Once we have the probabilities, we can multiply each by the total number of M&Ms (24) to find the number of M&Ms of each color.
This approach ensures that the distribution of M&Ms aligns with the given probabilities, providing a clear and logical solution to the problem.