14. A neuron makes three synapses on a muscle cell to produce a sudden movement. However, each
synapse is unreliable and only conveys a signal with a probability of 0.5. Successful signal
propagation by any one of the three synapses will result in muscle contraction. What is the probability
that the muscle will contract when the neuron fires?
a. 7/8
b. 3/2
c. 3/8
d. 1/8
Neuron Synapses Muscle Contraction Probability Explained
A neuron forms three independent synapses on a muscle cell, each transmitting a signal with probability 0.5. Muscle contraction occurs if at least one synapse succeeds, making this a classic “1 – probability of all failures” problem relevant to CSIR NET Life Sciences neuroscience topics.
The probability of failure at one synapse is 1 – 0.5 = 0.5. For all three to fail independently: (0.5)³ = 0.125 or 1/8. Thus, contraction probability is 1 – 0.125 = 0.875 or 7/8.
Option Analysis
- a. 7/8: Correct. Matches 1 – (0.5)³ = 7/8, as any single success triggers contraction.
- b. 3/2: Incorrect. Exceeds 1.0 (impossible probability); likely confuses addition with independent events.
- c. 3/8: Incorrect. Equals exactly one success: 3 × (0.5)³ = 3/8, ignoring multiple successes.
- d. 1/8: Incorrect. Probability all fail: (0.5)³ = 1/8, opposite of contraction event.
CSIR NET Exam Relevance
This question tests binomial probability in synaptic transmission reliability, a key concept in Unit 7 (System Physiology – Animal) for CSIR NET Life Sciences. Unreliable synapses (failure rates ~0.5 observed in studies) highlight redundancy in neuromuscular junctions for robust muscle contraction.
