If two switches `S_1a n dS_2` have respectively 90% and 80% chances of working. Find the probabilities that each of eth following circuits will work.

An electrical system has open-closed switches S_1, S_2a n dS_3 as shown in fig. The switches operate independently of one another and the current will flow from AtoB either if S_1 is closed or if both S_2a n dS_3 are closed. If P(S_1)=P(S_2)=P(S_3)=1//2, then find the probability that the circuit will work. fig

A speaks truth in 80% of the cases while B speaks truth in 60% of the cases. Find the probability that they will contradict each other while stating the same fact.

The percentage of monthly targets achieved in producing a certaina type of bolts in a company for differen months is given in the following tabel: Find the probability that the company achieved 80% of the monthly target in producing the bolts.

On a certain day the chance of rain is 80% in Delhi and 30% in Hyderabad.Assume that the chance of rain in the two cities is independent. What is the probability that it will not rain in either city?

A company has two plants to manufacture bicycles. The first plant manufactures 60% of bicycles and the second 40%. Also 80% of the bicycles are rated of standard qaulity at the first plant and 90% of the standard qaulity at the second plant. A bicycle is picked up at random and found to be of standard quality. Find the probability that it is produced from first plant.