Probability Question 14
Question: A and B toss a fair coin each simultaneously 50 times. The probability that both of them will not get tail at the same toss is
Options:
A) $ {{(3/4)}^{50}} $
B) $ {{(2/7)}^{50}} $
C) $ {{(1/8)}^{50}} $
D) $ {{(7/8)}^{50}} $
Show Answer
Answer:
Correct Answer: A
Solution:
For each toss, there are four choices:
(i) A gets head, B gets head
(ii) A gets tail, B gets head
(iii) A gets head, B gets tail
(iv) A gets tail, B gets tail Thus, exhaustive number of ways is $ 4^{50} $ .
Out of the four choices listed above, (iv) is not favorable to the required event in a toss.
Therefore, favorable number of cases is $ 3^{50} $ . Hence, the required probability is $ {{(3/4)}^{50}} $ .
BETA
