Answer to Question #169797 in Statistics and Probability for kk

Question

5. A fair die is rolled until a 6 occurs. Compute the probability that (a) 10 rolls are needed.

(b) an odd number of rolls is needed. 

Answer 1

a) The probability of getting 6 in the first roll P(1) is $\frac{1} {6}$

The probability of getting 6 in the second roll P(2) is $\frac{5}{6}×\frac{1} {6}$

Thus the probability of P(10);

$\frac{5}{6} ×\frac{5}{6}×\frac{5}{6}×\frac{5}{6}×\frac{5}{6}×\frac{5}{6}×\frac{5}{6}×\frac{5}{6}×\frac{5}{6}×\frac{1 }{6}$

=$\frac{4}{125}$

b)an odd number P(1) P(3)P(5)

$\frac{5}{6}×\frac{5}{6}×\frac{5}{6}×\frac{1 }{6}$

=$\frac{125}{1296}$