Statistics And Probability Question 47
Question: A fair die is tossed eight times. The probability that a third six is observed on the eighth throw is
Options:
A) $ ^{7}C_2\frac{5^{5}}{6^{8}} $
B) $ ^{7}C_3\frac{5^{3}}{6^{8}} $
C) $ ^{7}C_6\frac{5^{6}}{6^{8}} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] The required event occurs if two sixes are observed in the first seven throws and a six is observed on the eight throw. If P is the probability that a six shows on the die, the number of throws n is 7, and X is the the number of times a six is observed, then $ X\tilde{\ }B(7,p). $ Therefore the required probability equals $ P(X=2) $ times the probability of getting a six on the eight throw, i.e., it equals $ {{(}^{7}}C_2p^{2}q^{5})(p)={{(}^{7}}C_2){{( \frac{1}{6} )}^{2}}{{( \frac{5}{6} )}^{5}}( \frac{1}{6} )=\frac{^{7}c_2(5^{5})}{6^{8}} $
BETA
