Question

Q3. There are 5 red sweets, 6 blue sweets and 9 yellow sweets in a bag.

Sarah takes a sweet at random.
She replaces it back and then
Take another sweet at random.
Work out the probability the both the sweets the same colour.

Answer 1

Step-by-step explanation:There are a total of 20 sweets in the bag (5 red + 6 blue + 9 yellow).

To find the probability that Sarah takes two sweets of the same color, we need to find the probability of her choosing a sweet of a specific color on her first pick and then the probability of her choosing another sweet of that same color on her second pick.

For example, if she chooses a red sweet on her first pick, the probability of that happening is 5/20, or 1/4. Then the probability of her choosing another red sweet on her second pick, given that she already picked one, is 4/20, or 2/10. Therefore the probability of her choosing two red sweets in a row is (1/4) * (2/10) = 1/20.

Similarly, the probability of her choosing two blue sweets in a row is (6/20) * (5/20) = 3/50.

The probability of her choosing two yellow sweets in a row is (9/20) * (8/20) = 9/100.

The probability of her choosing two sweets of the same color is the sum of the probability of her choosing two red sweets, two blue sweets, or two yellow sweets in a row.

P(Two same color) = 1/20 + 3/50 + 9/100 = 11/50

So, the probability of her choosing two sweets of the same color is 11/50.