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Difficulty: MediumCompound Probability

A supply room contains 25 identical-looking computer mice, of which 10 are wireless and 15 are wired. If an IT technician randomly selects two mice from the room one after the other without replacement, what is the probability that both selected mice are wireless? (Express your answer as a decimal.)

Answer: 0.15

Answer

0.15
The correct answer is found by multiplying the probability of the first event by the conditional probability of the second event. First draw: 1025\frac{10}{25}. Second draw: 924\frac{9}{24}. Multiplying these gives 90600\frac{90}{600}, which simplifies exactly to 0.150.15.

Step-by-Step Solution

1
Determine the probability of the first event.
The probability of drawing the first wireless mouse is 1025\frac{10}{25}.
There are 10 target items (wireless mice) out of 25 total items.
2
Determine the probability of the second event given the first event occurred.
The probability of drawing a second wireless mouse is 924\frac{9}{24}.
Because the selection is without replacement, one wireless mouse has been removed, leaving 9 wireless mice out of 24 total mice.
3
Calculate the compound probability.
1025×924=0.15\frac{10}{25} \times \frac{9}{24} = 0.15
For dependent events occurring in sequence, multiply the probability of the first event by the conditional probability of the second event.

Key Concept

Compound Probability (Dependent Events)
Estimated Time:1m 0s
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Topics

Compound Probability

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