A bag contains 4 good and 2 bad apples.
Two apples are picked at random.
Find the probability of picking:
(b) 2 bad apples.

Question

A bag contains 4 good and 2 bad apples. Two apples are picked at random. Find the probability of picking: (b) 2 bad apples.

UpStudy AI · Accepted Answer

**Step 1: Identify the Total Outcomes**  
The total number of ways to pick any 2 apples from 6 is given by the combination:  
$$
\binom{6}{2} = \frac{6 \times 5}{2 \times 1} = 15.
$$

**Step 2: Identify the Favorable Outcomes**  
There are 2 bad apples available, and we need to pick both. The number of ways to pick 2 bad apples from 2 is:  
$$
\binom{2}{2} = 1.
$$

**Step 3: Compute the Probability**  
The probability of picking 2 bad apples is given by the ratio of favorable outcomes to total outcomes:  
$$
P(\text{2 bad apples}) = \frac{\binom{2}{2}}{\binom{6}{2}} = \frac{1}{15}.
$$
The probability of picking 2 bad apples is $$ \frac{1}{15} $$.

A bag contains 4 good and 2 bad apples.
Two apples are picked at random.
Find the probability of picking:
(b) 2 bad apples.

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