Q. 14  In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is

              (A)  10^{-1}

              (B)  \left ( \frac{1}{5} \right )^{5}

              (C)  \left ( \frac{9}{10} \right )^{5}

              (D)  \frac{9}{10}

Answers (1)

Let X represent a number of defective bulbs out of 5 bulbs.

Probability of getting a defective bulb =P

        P=\frac{10}{100}=\frac{1}{10}

        q=1-P=1-\frac{1}{10}=\frac{9}{10}

X has a binomial distribution,n=5

\therefore \, \, \, \, P(X=x)=^nC_x.q^{n-x}.p^x

                P(X=x)=^5C_x.(\frac{9}{10})^{5-x} . (\frac{1}{10})^{x}

                    P(non\,of \,bulb\,is\, defective \,)=P(X=0)

                                                                               =^{5}C_0 (\frac{9}{10})^{5}\frac{1}{10}^0

                                                                              =1.\frac{9}{10}^5

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

The correct answer is C.

Most Viewed Questions

Related Chapters

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
Buy Now
NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions