Question:
A box contains 20 percent defective bulbs. Five bulbs are randomly chosen. Find the probability that exactly 3 are defective.
A box contains 20 percent defective bulbs. Five bulbs are randomly chosen. Find the probability that exactly 3 are defective.
Show Hint
Use binomial probability distribution for repeated trials with success/failure outcomes.
Updated On: Mar 19, 2025
- \( \frac{32}{625} \)
- \( \frac{32}{125} \)
- \( \frac{16}{625} \)
- \( \frac{16}{125} \)
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Binomial Probability Formula
\[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \] Given: \( n = 5, k = 3, p = 0.2 \), \[ P(X = 3) = \binom{5}{3} (0.2)^3 (0.8)^2 \] Step 2: Computation
\[ = 10 \times (0.008) \times (0.64) \] \[ = 10 \times 0.00512 = 0.0512 \] \[ = \frac{32}{625} \] Thus, the correct answer is \( \frac{32}{625} \).
\[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \] Given: \( n = 5, k = 3, p = 0.2 \), \[ P(X = 3) = \binom{5}{3} (0.2)^3 (0.8)^2 \] Step 2: Computation
\[ = 10 \times (0.008) \times (0.64) \] \[ = 10 \times 0.00512 = 0.0512 \] \[ = \frac{32}{625} \] Thus, the correct answer is \( \frac{32}{625} \).
Was this answer helpful?
0
0
Top Questions on Probability
- A die is rolled. What is the probability of getting a number less than or equal to 4?
- MHT CET - 2025
- Mathematics
- Probability
- A bag contains 5 red balls and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are red?
- MHT CET - 2025
- Mathematics
- Probability
- If \( A \) and \( B \) are two non-mutually exclusive events such that \( P(A | B) = P(B | A) \), then:
- KCET - 2025
- Mathematics
- Probability
- Meera visits only one of the two temples A and B in her locality. Probability that she visits temple A is \( \frac{2}{5} \). If she visits temple A, the probability that she meets her friend is \( \frac{1}{3} \). The probability that she meets her friend, whereas it is \( \frac{2}{7} \) if she visits temple B. Meera met her friend at one of the two temples. The probability that she met her friend at temple B is:
- KCET - 2025
- Mathematics
- Probability
- If \( A \) and \( B \) are two events such that \( A \subseteq B \) and \( P(B) \neq 0 \), then which of the following is correct?
- KCET - 2025
- Mathematics
- Probability
View More Questions
Questions Asked in AP EAMCET exam
- Consider the reaction: \(C_2H_5Cl(g) \rightarrow 2C(g) + 5H(g) + Cl(g)\), where \(\Delta H = 3047 \, {kJ mol}^{-1}\). The bond dissociation enthalpy (\(\Delta_{{bond}} H\)) values of C–Cl and C=C bonds are 431 and 414 kJ mol\(^{-1}\), respectively. What is the average bond enthalpy of C–H in kJ mol\(^{-1}\)?
- AP EAMCET - 2024
- Stereoisomers
- If the first ionisation enthalpy of Li, Be and C respectively are 520, 899, 1086 kJ/mol, the first ionisation enthalpy (in kJ/mol) of B will be
- AP EAMCET - 2024
- Periodic Table
- Evaluate the sum: \[ \sin^2 18^\circ + \sin^2 24^\circ + \sin^2 36^\circ + \sin^2 42^\circ + \sin^2 78^\circ + \sin^2 90^\circ + \sin^2 96^\circ + \sin^2 102^\circ + \sin^2 138^\circ + \sin^2 162^\circ. \]
- AP EAMCET - 2024
- Trigonometry
- The general solution of \( 4 \cos 2x - 4 \sqrt{3} \sin 2x + \cos 3x - \sqrt{3} \sin 3x + \cos x - \sqrt{3} \sin x = 0 \) is:
- AP EAMCET - 2024
- Trigonometric Identities
- If \( (\alpha, \beta, \gamma) \) are the direction cosines of an angular bisector of two lines whose direction ratios are (2,2,1) and (2,-1,-2), then \( (\alpha + \beta + \gamma)^2 \) is:
- AP EAMCET - 2024
- Coordinate Geometry
View More Questions