Question

A batch of one hundred cars is inspected by testing four randomly selected cars. If one of the four is defective, the batch is rejected. What is the probability that the batch is accepted if it contains five defective cars?

Answer 1

Answer: The probability that the batch is accepted is 0.812.

Step-by-step explanation:

Since we have given that

Number of defective cars = 5

Total number of cars = 100

Probability of getting first car non defective = $\dfrac{95}{100}$

probability of getting second car non defective = $\dfrac{94}{99}$

Probability of getting third car non defective =  $\dfrac{93}{98}$

Probability of getting fourth car non defective = $\dfrac{92}{97}$

Using the multiplication rule, probability that the batch is accepted is given by

$\dfrac{95}{100}\times \dfrac{94}{99}\times \dfrac{93}{98}\times \dfrac{92}{97}\\\\=0.812$

Hence, the probability that the batch is accepted is 0.812.