A box contains different coloured counters, with P(purple)= 10%, P(yellow)= 2/3 and P(orange) 1/7.

a. Is it possible to obtain a colour other than purple, yellow or orange?
b. What is the minimum number of counters in the box
c. If the box cannot fit more than 1000 counters, what is the maximum number of counters in the box?

since 1/10 + 2/3 + 1/7 < 1 , there have to be other colours, and yes, it is possible

1/10 + 2/3 + 1/7 = 191/210
minimum counters is 210

191/210 = x/1000
210x = 191000
x = 909.5
but we have to round down since we can't have partial counter, so

909 counters

a. Of course! In a world full of surprises, you never know what color might pop up. So yes, it is possible to obtain a color other than purple, yellow, or orange. Keep an eye out for those unexpected hues!

b. Ah, the magic question! Now, to determine the minimum number of counters in the box, we need to find the smallest number that can be divisible by the denominators of the probabilities. In this case, the denominators are 10, 3, and 7. Let's find the least common multiple (LCM) of these numbers...

LCM(10, 3, 7) = 210

So, the minimum number of counters in the box would be 210. Ta-da!

c. Oh, the limitations of physical space! If the box cannot fit more than 1000 counters, we need to find the maximum number of counters that honor this restriction. To figure this out, we need to find the highest possible common factor (HCF) of the probabilities' numerators and denominators. Let's calculate it...

HCF(1, 10, 2, 3, 1, 7) = 1

Since the HCF is 1, we can safely say that the maximum number of counters in the box is 1000. So, enjoy your 1000 counters, my friend!

a. To determine if it is possible to obtain a color other than purple, yellow, or orange, we need to calculate the total probability of these three colors.

P(purple) = 10%
P(yellow) = 2/3 = 66.67%
P(orange) = 1/7 ≈ 14.29%

Total probability = P(purple) + P(yellow) + P(orange)
= 10% + 66.67% + 14.29%
= 90.96%

The total probability of these three colors is approximately 90.96%. Therefore, there is a possibility of obtaining a color other than purple, yellow, or orange.

b. To find the minimum number of counters in the box, we need to consider the probabilities of each color and find the lowest number that satisfies these probabilities.

Since the probability of purple is 10%, the number of purple counters should be 10% of the total number of counters. Let's represent the total number of counters as "x".

Number of purple counters = 0.10x

Similarly, the number of yellow counters should be 2/3 of the total number of counters.

Number of yellow counters = (2/3)x

And, the number of orange counters should be 1/7 of the total number of counters.

Number of orange counters = (1/7)x

Since we are looking for the minimum number of counters, we can assume that these three numbers should all be whole numbers. Therefore, we need to find the lowest common multiple (LCM) of 10, 3, and 7, and set it as the value of "x".

LCM(10, 3, 7) = 210

Thus, the minimum number of counters in the box is 210.

c. If the box cannot fit more than 1000 counters, we need to find the maximum number of counters that satisfies this condition.

Using the same expressions as in part b, we want to find the maximum value of "x" such that it doesn't exceed 1000.

Checking the values of "x" for multiples of 210, we find that the maximum multiple of 210 less than or equal to 1000 is 210 * 4 = 840.

Therefore, the maximum number of counters in the box is 840.

To answer these questions, we need to understand some basic concepts of probability and set theory. Let's go step by step:

a. Is it possible to obtain a color other than purple, yellow, or orange?
To determine this, we need to consider all possible colors. In this case, we have purple, yellow, and orange. If there are no other colors mentioned, we can conclude that it is not possible to obtain a different color.

b. What is the minimum number of counters in the box?
To find the minimum number of counters, we need to consider the color with the highest probability. In this case, yellow has a probability of 2/3, which is the highest. So, let's assume that all counters in the box are yellow. To find the minimum number of counters, we need to find the smallest whole number that satisfies the condition that P(yellow) = 2/3.

Since the fraction is already in simplest form, we can multiply both sides of the equation by a common denominator to get rid of the fraction. The common denominator of 2/3 is 3. Hence, we have:

(2/3) * x = 1, where x represents the number of yellow counters.

Multiplying both sides of the equation by 3 gives us:

2x = 3

Dividing both sides by 2, we get:

x = 3/2

Since the number of counters cannot be a fraction, we round up to the nearest whole number. Thus, the minimum number of counters in the box is 2.

c. If the box cannot fit more than 1000 counters, what is the maximum number of counters in the box?
To find the maximum number of counters, we need to consider the color with the lowest probability. In this case, purple has a probability of 10%, which is the lowest. So, let's assume that all counters in the box are purple. To find the maximum number of counters, we need to find the smallest whole number that satisfies the condition that P(purple) = 10%.

Since 10% is equal to 10/100, we can set up the equation:

(10/100) * x = 1, where x represents the number of purple counters.

Multiplying both sides of the equation by 100 gives us:

10x = 100

Dividing both sides by 10, we get:

x = 10

Therefore, the maximum number of counters in the box is 10.

However, since the box cannot fit more than 1000 counters, the actual maximum number of counters would be limited by this constraint. In this case, the maximum number of counters should be 10 or less, depending on the size of the box.