A bag contains 5 good and 3 bad apples.
Two apples are picked at random.
Find the probability of picking:
(b) 2 bad apples.

Question

A bag contains 5 good and 3 bad apples. Two apples are picked at random. Find the probability of picking: (b) 2 bad apples.

UpStudy AI · Accepted Answer

We are given a bag with 5 good apples and 3 bad apples, making a total of 8 apples.

### Step 1: Total number of ways to pick 2 apples

The total number of ways to choose 2 apples from 8 is given by the combination formula:
$$
\binom{8}{2} = \frac{8 \times 7}{2 \times 1} = 28
$$

### Step 2: Number of ways to pick 2 bad apples

The number of ways to choose 2 bad apples from the 3 bad apples is:
$$
\binom{3}{2} = \frac{3 \times 2}{2 \times 1} = 3
$$

### Step 3: Calculate the probability

The probability of picking 2 bad apples is the ratio of the favorable outcomes to the total outcomes:
$$
P(\text{2 bad apples}) = \frac{\binom{3}{2}}{\binom{8}{2}} = \frac{3}{28}
$$

Thus, the probability of picking 2 bad apples is $$ \frac{3}{28} $$.
The probability of picking 2 bad apples is $$ \frac{3}{28} $$.

A bag contains 5 good and 3 bad apples.
Two apples are picked at random.
Find the probability of picking:
(b) 2 bad apples.

Upstudy AI Solution

Answer

Solution

Step 1: Total number of ways to pick 2 apples

Step 2: Number of ways to pick 2 bad apples

Step 3: Calculate the probability

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