There is a toy train that can make 10 musical sounds. It makes 2 musical…
20232025
There is a toy train that can make 10 musical sounds. It makes 2 musical sounds after being defective. What is the probability that same musical sound would be produced 5 times consecutively?
- A.
1/4
- B.
1/8
- C.
1/32
- D.
1/16
Attempted by 23 students.
Show answer & explanation
Correct answer: D
Key idea: after the toy becomes defective it produces 2 possible sounds, each equally likely (probability 1/2).
Method 1 — Counting outcomes: Each of the five plays can be one of 2 sounds, so there are 2^5 = 32 equally likely sequences. Only two sequences have all five the same (all first sound or all second sound). Therefore probability = 2/32 = 1/16.
Method 2 — Conditional probability: Fix the first sound (any). The next four must match it, each with probability 1/2, so probability = (1/2)^4 = 1/16.
Final answer: 1/16.
This corresponds to the choice '1/16'.