A quality assurance technician randomly selects 2 microprocessors from a batch of 16 micro… — GMAT

A quality assurance technician randomly selects 2 microprocessors from a batch of $16$ microprocessors, of which $6$ were manufactured at Facility A and $10$ were manufactured at Facility B. The selections are made one after another without replacement. What is the probability that both selected microprocessors were manufactured at Facility A?

Cevap: 0.125

Cevap

The probability that both selected microprocessors were manufactured at Facility A is 0.125 (or 1/8).

Because the selections are made without replacement, the outcome of the first draw changes the pool of available microprocessors for the second draw. The probability of choosing a Facility A microprocessor first is

\frac{6}{16} = \frac{3}{8}

. Following that selection,

5

Facility A microprocessors remain among

15

total microprocessors, giving a conditional probability of

\frac{5}{15} = \frac{1}{3}

for the second selection. Multiplying these dependent probabilities yields

\frac{3}{8} \times \frac{1}{3} = \frac{1}{8} = 0.125

Adım Adım Çözüm

Determine the probability of selecting a Facility A microprocessor on the first draw.

P(\text{First is Facility A}) = \frac{6}{16} = \frac{3}{8}

There are 6 microprocessors from Facility A out of 16 total microprocessors.

Determine the conditional probability of selecting a Facility A microprocessor on the second draw.

P(\text{Second is Facility A} \mid \text{First is Facility A}) = \frac{5}{15} = \frac{1}{3}

Since the selection is made without replacement, 5 Facility A microprocessors remain out of a reduced total of 15 microprocessors.

Multiply the dependent probabilities to find the combined probability.

P(\text{Both are Facility A}) = \frac{3}{8} \times \frac{1}{3} = \frac{3}{24} = \frac{1}{8} = 0.125

The joint probability of sequential dependent events is the product of the initial probability and the conditional probability.

Anahtar Kavram

Probability of Dependent Events (Sampling without Replacement)

Tahmini Süre:1m 30s

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