A supply cabinet contains 10 identical safety helmets, of which 2 are yellow and 8 are whi… — Armed Services Vocational Aptitude Battery (ASVAB)

A supply cabinet contains $10$ identical safety helmets, of which $2$ are yellow and $8$ are white. A construction worker randomly selects a helmet, records its color, returns it to the cabinet, and then randomly selects a second helmet. What is the probability of selecting a yellow helmet both times? Express your answer as a decimal.

Cevap: 0.04

Cevap

0.04

Since the helmet is replaced after the first draw, the two events are independent. The probability of drawing a yellow helmet is

\frac{2}{10}

(or

0.2

). To find the probability of drawing a yellow helmet twice in a row, multiply the probabilities of the two independent events:

0.2 \times 0.2 = 0.04

Adım Adım Çözüm

Find the probability of the first event.

\frac{2}{10}

0.2

There are

2

yellow helmets out of

10

total.

Find the probability of the second event.

\frac{2}{10}

0.2

Because the helmet was replaced, the total number and the number of yellow helmets remain the same.

Calculate the compound probability.

0.04

For independent events, multiply the individual probabilities together:

0.2 \times 0.2 = 0.04

Anahtar Kavram

The probability of two independent events occurring is the product of their individual probabilities:

P(A \text{ and } B) = P(A) \times P(B)

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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