Neurons release a neurotransmitter following electrical activation in a probabil
ID: 1998471 • Letter: N
Question
Neurons release a neurotransmitter following electrical activation in a probabilistic manner. Suppose that a neuron successfully releases a neurotransmitter following electrical activation with a probability of 0.7. Assume that the probability of neurotransmitter release following each activation is independent of that on all other activations. Find the probability that the neuron fails to release neurotransmitter at least once in 5 activations. Suppose that the neuron is activated 5 times, find the probability that the neuron fails to release neurotransmitter (event F) on the first and third activations and successfully releases neurotransmitter (event S) on the second, fourth and fifth activations. Suppose that the neuron is activated 5 times, find the probability that the neuron fails to release neurotransmitter (event F) twice and successfully releases neurotransmitter (event S) three times.Explanation / Answer
(a) Probability that it fail to release neutrotransmitter in atleast once in 5 activation=1-probability of releasing every time successfully=1-(0.7)^5=0.83
(b)probability of failing in 1st and 3rd activaton and successful everytime=0.3*0.7*0.3*0.7*0.7=0.03
(c)Probability of failing 2 times and success 3 times=0.3^2*0.7^3*10=0.3087