A toy train can make 10 sounds sound changes after every 4 minute now ...
(1/2)*(1/2)*(1/2)*(1/2)+ (1/2)*(1/2)*(1/2)*(1/2)=(1/8)
thus 1 out of 8 ans
View all questions of this testA toy train can make 10 sounds sound changes after every 4 minute now ...
To find the probability of the same sound being repeated 4 times consecutively, we need to consider the number of possible sequences that satisfy this condition and divide it by the total number of possible sequences.
Let's break down the problem step by step:
1. Total number of possible sequences:
Since the toy train can make 2 sounds now, there are 2 options for each sound. As the sound changes after every 4 minutes, there are a total of 10 sound changes in 40 minutes (10 * 4 = 40). Therefore, the total number of possible sequences is 2^10 = 1024.
2. Number of sequences with the same sound repeated 4 times consecutively:
To calculate this, we need to consider the position of the repeated sound within the sequence. Since the sound needs to be repeated 4 times consecutively, there are only 7 possible positions where the repeated sound can start (1st, 2nd, 3rd, ..., 7th). For each starting position, there is only one possible sequence of 4 repeated sounds. Therefore, the total number of sequences with the same sound repeated 4 times consecutively is 7.
3. Probability calculation:
To find the probability, we divide the number of sequences with the same sound repeated 4 times consecutively by the total number of possible sequences.
Probability = (Number of sequences with 4 consecutive repeated sounds) / (Total number of possible sequences)
= 7 / 1024
≈ 0.0068
Since the probability is in decimal form, it can be represented as a fraction by multiplying both the numerator and denominator by 1000:
Probability = 7 / 1024 ≈ 6.8 / 1000
Therefore, the answer is approximately 6.8 in fraction form, which is equivalent to 1 out of 147 (rounded to the nearest whole number).
Hence, the correct answer is option B) 8.