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?

  1. A.

    1/4

  2. B.

    1/8

  3. C.

    1/32

  4. D.

    1/64

  5. E.

    None of the above

Attempted by 20 students.

Show answer & explanation

Correct answer: E

Step-by-Step Solution

To find the probability of the same musical sound being produced 5 times consecutively, we analyze the problem as a sequence of independent events.

  1. Understand the conditions:

    • The toy now produces only 2 possible sounds.

    • The probability of either sound occurring in a single instance is 1/2.

    • We want to find the probability that the same sound repeats 5 times in a row.

  2. Calculate for a single sound:

    • If we choose a specific sound (e.g., sound A), the probability of it occurring 5 times consecutively is (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = (1/2)^5 = 1/32.

  3. Account for both possible sounds:

    • Since there are 2 different sounds, the event can happen in two mutually exclusive ways:

      • Case (a): Sound A is produced 5 times consecutively.

      • Case (b): Sound B is produced 5 times consecutively.

    • The probability for Case (a) is 1/32.

    • The probability for Case (b) is 1/32.

  4. Find the total probability:

    • Total Probability = P(Case a) + P(Case b)

    • Total Probability = 1/32 + 1/32 = 2/32 = 1/16.

Explore the full course: Cognizant Preparation