Question

One in nine ships is likely to be wrecked, when they are set on sail. When $6$ ships set on sail, the probability for exactly $3$ will not arrive safely is:

• A. $\frac{25\times 8^3}{9^6}$
• B. $1-\frac{1}{9^6}$
• C. ${}^6{C}_3\left(\frac{8^3}{9^6}\right)$
• D. ${}^6{C}_3\left(\frac{8^6}{9^6}\right)$

Answer 1

The correct option is C ${}^6{C}_3\left(\frac{8^3}{9^6}\right)$

$P\left(\text{wreck}\right)=p=\frac{1}{9},n=6,P\left(\text{safe arrival}\right)=q=\frac{8}{9}$
Probability for exactly $3$ will not arrive safely
$={}^6{C}_3{\left(\frac{1}{9}\right)}^3{\left(\frac{8}{9}\right)}^3={}^6{C}_3\left(\frac{8^3}{9^6}\right)$