A box contains 100 bulbs, out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective is

Question

A box contains 100 bulbs, out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective is (A) ( (1/10))5 (B) ( (1/2))5 (C)  (9/10) (D) ( (9/10))5

Tardigrade Admin · Accepted Answer

Let probability of defective bulb, p=(10/100)=(1/10)=0.1 and probability of non-defective bulb, q=1-0.1=0.9 Here, n=5 ∴ P [none is defective] =P(X=0) = 5 C0(0.1)0(0.9)5=1 ×(0.9)5=((9/10))5

Q. A box contains $100$ bulbs, out of which $10$ are defective. A sample of $5$ bulbs is drawn. The probability that none is defective is

$(\frac{1}{10})^{5}$

$(\frac{1}{2})^{5}$

$\frac{9}{10}$

$(\frac{9}{10})^{5}$

Let probability of defective bulb,
$p = \frac{10}{100} = \frac{1}{10} = 0.1$
and probability of non-defective bulb,
$q = 1 - 0.1 = 0.9$
Here, $n = 5$
$∴ P$ [none is defective] $= P (X = 0)$
$=^{5} C_{0} (0.1)^{0} (0.9)^{5} = 1 \times (0.9)^{5} = (\frac{9}{10})^{5}$

Q. A box contains 100 bulbs, out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective is

(101​)5

(21​)5

109​

(109​)5