Question

4 persons are asked the same question by an interviewer. If each has independent probability $\frac{1}{6}$ of answering the question correctly. The probability that at least one answers correctly is:

• A. $\frac{2}{3}$
• B. ${\left(\frac{1}{6}\right)}^4$
• C. $1-{\left(\frac{5}{6}\right)}^4$
• D. $1-{\left(\frac{1}{6}\right)}^4$

Answer 1

The correct option is C

$1-{\left(\frac{5}{6}\right)}^4$

n = 4 (r person)

x = number of correct ones

$P(x\ge 1)=1-P(x=0)=1-{(1-\frac{1}{6})}^4=1-{\left(\frac{5}{6}\right)}^4$