Question

If 20% of the bolts produced by a machine are defective. Find the probability that out of 4 bolts drawn at most two are defective.


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Answer 1

Given:

20% of the bolts produced by a machine are defective

To Find:

Probability that out of 4 bolts drawn at most two are defective.

Solution:

ATQ

Number of bolts drawn = n = 4

Probability of defective bolts = p = 20% = 20/100 = 1/5

Probability of not defective bolts = q = 1 - 1/5 = 4/5

Probability of atmost 2 items are defective :-

= P(X=0) + P(X=1) + P(X=2)

= 4C0×p⁰×q⁴ + 4C1×p¹×q³ + 4C2×p²×q²

= 1×1×(4/5)⁴ + 4×1/5×(4/5)³ + 6×(1/5)²×(4/5)²

= 256/625 + 256/625 + 96/625

= 608/625

= 0.9728

Hence, it is the required answer.

Answer 2

Answer:

0.9728 is answer

Step-by-step explanation:

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