The decimal number corresponding to a sequence of n binary digits a 0 , a 1 , ....... , a n − 1 , where each a i is either 0 or 1, is defined to be a 0 2 0 + a 1 2 1 + ....... + a n − 1 2 n − 1 For example, the sequence 0 1 1 0 is equal to 6 (= 0·2 0 + 1·2 1 + 1·2 2 + 0·2 3 ). Suppose a fair coin is tossed nine times. Replace the resulting sequence of H’s and T’s with a binary sequence of 1’s and 0’s (1 for H, 0 for T). For how many sequences of tosses will the decimal corresponding to the observed set of heads and tails exceed 256?
The decimal number corresponding to a sequence of n binary digits a 0 , a 1 , ....... , a n − 1 , where each a i is either 0 or 1, is defined to be a 0 2 0 + a 1 2 1 + ....... + a n − 1 2 n − 1 For example, the sequence 0 1 1 0 is equal to 6 (= 0·2 0 + 1·2 1 + 1·2 2 + 0·2 3 ). Suppose a fair coin is tossed nine times. Replace the resulting sequence of H’s and T’s with a binary sequence of 1’s and 0’s (1 for H, 0 for T). For how many sequences of tosses will the decimal corresponding to the observed set of heads and tails exceed 256?
Solution Summary: The author explains that there are 255 sequences of tosses that will be the decimal corresponding to the observed set of heads and tails exceed 256.
The decimal number corresponding to a sequence of n binary digits
a
0
,
a
1
,
.......
,
a
n
−
1
, where each
a
i
is either 0 or 1, is defined to be
a
0
2
0
+
a
1
2
1
+
.......
+
a
n
−
1
2
n
−
1
For example, the sequence 0 1 1 0 is equal to 6 (= 0·20 + 1·21 + 1·22 + 0·23). Suppose a fair coin is tossed nine times. Replace the resulting sequence of H’s and T’s with a binary sequence of 1’s and 0’s (1 for H, 0 for T). For how many sequences of tosses will the decimal corresponding to the observed set of heads and tails exceed 256?
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.