Suppose a machine produces metal parts that contain some defective parts with probability $0.05$ . How many parts should be produced in order that probability of at least one part being defective is $1 / 2$ or more? (Given ${log}_{10} 95 = 1.977$ and ${log}_{10} 2 = 0.3)$

11

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Solution

The correct options are
B $12$
C $11$
Probability of at least one part being defective
$= 1 -$ Probability of no part defective
$= 1 - (0.95)^{n} \geq \frac{1}{2}$
So $(0.95)^{n} \leq \frac{1}{2}$

Taking $log$ on both sides with base $10$ , we get
$n [{log}_{10} 95 - 2] \leq {log}_{10} \frac{1}{2}$
$\Rightarrow n \leq \frac{300}{23} \leq 13$
so $n = 11, 12$

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Similar questions

Q. Suppose a machine produces metal parts that contain some defective parts with probability

0.05

. How many parts should be produced in order that the probability of atleast one part being defective is

\frac{1}{2}

or more?

(Given that,

{log}_{10} 95 = 1.977

and

{log}_{10} 2 = 0.3

)

Q. Suppose a machine produces metal parts that contain some defective parts with probability

0.05

. How many parts should be produced in order that the probability of at least one part being defective is

\frac{1}{2}

or more?
(Given

{log}_{10} 95 = 1.977

and

{log}_{10} 2 = 0.3)

Q. Question 19
Over the past 200 working days, the number of defective parts produced by a machine is given in the following table.

\begin{matrix} N u m b e r o f & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 d e f e c t i v e p a r t s D a y s & 50 & 32 & 22 & 18 & 12 & 12 & 10 & 10 & 10 & 10 & 8 & 6 & 6 & 2 \end{matrix}

Determine the probability that tomorrow’s output will have:
(i) No defective part.
(ii) Atleast one defective part.
(iii) Not more than 5 defective parts.
(iv) More than 13 defective parts.

Over the past 200 working days, the number of defective parts produced by a machine is given in the following table:

No of defective parts	0	1	2	3	4	5	6	7	8	9	10	11	12	13
Days	50	32	22	18	12	12	10	10	10	8	6	6	2	2

Determine the probability that tomorrow's output will have at least one defective part.

The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts are selected randomly and inspected, then the probability that at least two parts will be defective is (round off to two decimal places).

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Suppose a machine produces metal parts that contain some defective parts with probability 0.05. How many parts should be produced in order that probability of at least one part being defective is 1/2 or more? (Given log1095=1.977 and log102=0.3)

The correct options are B 12 C 11Probability of at least one part being defective=1− Probability of no part defective=1−(0.95)n≥12So (0.95)n≤12Taking log on both sides with base 10, we getn[log1095−2]≤log1012⇒n≤30023≤13so n=11,12

Suppose a machine produces metal parts that contain some defective parts with probability $0.05$ . How many parts should be produced in order that probability of at least one part being defective is $1 / 2$ or more? (Given ${log}_{10} 95 = 1.977$ and ${log}_{10} 2 = 0.3)$