Try Magic Notes and save time.Try it free
Try Magic Notes and save timeCrush your year with the magic of personalized studying.Try it free
Question

# When commercial aircraft are inspected, wing cracks are reported as nonexistent, detectable, or critical. The history of a particular fleet indicates that 70% of the planes inspected have no wing cracks, 25% have detectable wing cracks, and 5% have critical wing cracks. Five planes are randomly selected. Find the probability that one has a critical crack, two have detectable cracks, and two have no cracks.

Solution

Verified
Step 1
1 of 2

Definition multinomial distribution:

$p(y_1,y_2,...,y_k)=\dfrac{n!}{y_1!y_2!...y_k!}p_1^{y_1}p_2^{y_2}...p_k^{y_k}$

Then we obtain:

$p(2,2,1)=\dfrac{5!}{2!2!1!}0.70^{2} 0.25^2 0.05^1\approx 0.0459$

## Recommended textbook solutions

#### Probability and Statistics for Engineers and Scientists

9th EditionISBN: 9780321629111 (9 more)Keying E. Ye, Raymond H. Myers, Ronald E. Walpole, Sharon L. Myers
1,204 solutions

#### Mathematical Statistics with Applications

7th EditionISBN: 9780495110811 (1 more)Dennis Wackerly, Richard L. Scheaffer, William Mendenhall
3,341 solutions

#### The Practice of Statistics for the AP Exam

5th EditionISBN: 9781464108730 (1 more)Daniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor
2,433 solutions

#### Statistics and Probability with Applications

3rd EditionISBN: 9781464122163Daren S. Starnes, Josh Tabor
2,555 solutions