A portable lamp has 8 batteries, 3 of which are defective. If 2 are selected at random with replacement, find the probability that both are defective. Round your answer to two decimal places.
Question
A portable lamp has 8 batteries, 3 of which are defective. If 2 are selected at random with replacement, find the probability that both are defective. Round your answer to two decimal places.
Solution
To solve this problem, we need to use the concept of probability.
Step 1: Identify the total number of batteries and the number of defective batteries.
- Total number of batteries = 8
- Number of defective batteries = 3
Step 2: Calculate the probability of selecting one defective battery.
- Probability of selecting one defective battery = Number of defective batteries / Total number of batteries = 3/8 = 0.375
Step 3: Since the problem states that the selection is with replacement, this means after selecting the first battery, it is put back, so the total number of batteries remains the same. Therefore, the probability of selecting another defective battery remains the same = 0.375
Step 4: Calculate the probability of both batteries being defective.
- Since these are independent events, the probability of both events happening is the product of their individual probabilities.
So, the probability that both batteries are defective = Probability of first battery being defective * Probability of second battery being defective = 0.375 * 0.375 = 0.140625
Step 5: Round the answer to two decimal places.
So, the probability that both batteries are defective is approximately 0.14.
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