Alice placed 15 red sweets, 17 green sweets
and a few blue sweets in a bag. If the
probability of picking a blue sweet is find
a) the number of blue sweets in the bag
b) the probability of picking a green sweet
c) the probability of picking a red sweet

Question

Alice placed 15 red sweets, 17 green sweets
and a few blue sweets in a bag. If the
probability of picking a blue sweet is

find
a) the number of blue sweets in the bag
b) the probability of picking a green sweet
c) the probability of picking a red sweet

UpStudy AI · Accepted Answer

To solve the problem, we first need to determine the total number of sweets in the bag and the number of blue sweets.

### a) Finding the number of blue sweets

Let $$ b $$ be the number of blue sweets. The total number of sweets in the bag is:

$$
15 \text{ (red)} + 17 \text{ (green)} + b \text{ (blue)} = 32 + b
$$

The probability of picking a blue sweet is given as $$ \frac{9}{25} $$. The probability of picking a blue sweet can also be expressed as the ratio of the number of blue sweets to the total number of sweets:

$$
\frac{b}{32 + b} = \frac{9}{25}
$$

To solve for $$ b $$, we can cross-multiply:

$$
25b = 9(32 + b)
$$

Expanding the right side:

$$
25b = 288 + 9b
$$

Now, we can isolate $$ b $$:

$$
25b - 9b = 288
$$
$$
16b = 288
$$
$$
b = \frac{288}{16} = 18
$$

So, the number of blue sweets is $$ \boxed{18} $$.

### b) Finding the probability of picking a green sweet

Now that we know there are 18 blue sweets, we can find the total number of sweets:

$$
\text{Total sweets} = 15 + 17 + 18 = 50
$$

The probability of picking a green sweet is given by the ratio of the number of green sweets to the total number of sweets:

$$
\text{Probability of green sweet} = \frac{17}{50}
$$

Thus, the probability of picking a green sweet is $$ \boxed{\frac{17}{50}} $$.

### c) Finding the probability of picking a red sweet

Similarly, the probability of picking a red sweet is given by the ratio of the number of red sweets to the total number of sweets:

$$
\text{Probability of red sweet} = \frac{15}{50}
$$

This can be simplified:

$$
\frac{15}{50} = \frac{3}{10}
$$

Thus, the probability of picking a red sweet is $$ \boxed{\frac{3}{10}} $$.
a) There are 18 blue sweets. b) The probability of picking a green sweet is $$ \frac{17}{50} $$. c) The probability of picking a red sweet is $$ \frac{3}{10} $$.

Alice placed 15 red sweets, 17 green sweets
and a few blue sweets in a bag. If the
probability of picking a blue sweet is find
a) the number of blue sweets in the bag
b) the probability of picking a green sweet
c) the probability of picking a red sweet

Upstudy AI Solution

Answer

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Alice placed 15 red sweets, 17 green sweets and a few blue sweets in a bag. If the probability of picking a blue sweet is find a) the number of blue sweets in the bag b) the probability of picking a green sweet c) the probability of picking a red sweet

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Probability Questions

Alice placed 15 red sweets, 17 green sweets
and a few blue sweets in a bag. If the
probability of picking a blue sweet is find
a) the number of blue sweets in the bag
b) the probability of picking a green sweet
c) the probability of picking a red sweet