Question

the coffee machine in the pi cafe has three dispensers p,q, and r. the probabilities that each malfunctions on a given day are 0.007,0.003 and 0.001 respectively.find the probability that exact one of the dispensers malfunctions on a given day.

Answer 1

From the given data probability of malfunction is given by,

$P(p)=0.007\\ P(q)=0.003\\ P(r)=0.001\\$

And for each of the machines , probability of not malfunctioning is given by,

$P'(p)=1-0.007=0.993\\ P'(q)=1-0.003=0.997\\ P'(r)=1-0.001=0.999\\$

Since malfunctions are independent,

Probability that exact one of the dispensers malfunctions is given by,

$P(E)=P'(p)P'(q)P(r)+P'(p)P(q)P'(r)+P(p)P'(q)P'(r)\\ P(E)=0.993\times0.997\times0.001+0.993\times0.003\times0.999+0.007\times0.997\times0.999\\ P(E)=0.00099+0.00297+0.00697\\ P(E)=0.0109$