What is the probability that series circuit with three switches `S_1,\ S_2a n d\ S_3` with probabilities `1/3,1/2a n d3/4` respectively of functioning will work?

A company has estimated that the probabilities of success fro there products introduced in the market are 1/3,2/5a n d2/3 respectively. Assuming independence, find the probability that the three products are successful. none of the products is successful,

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

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

An electrical system has open-closed switches S_1, S_2 and S_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_2 and S_3 are closed. If P(S_1)=P(S_2)=P(S_3)=1//2, then find the probability that the circuit will work.

An automobile company uses three types of steel S_1, \ \ S_2\ a n d\ S_3 for producing three types of cars C_1,\ \ C_2\ a n d\ C_3 . Steel requirements (in tons) for each type of cars are given below: [[Steel Cars, C_1, C_2, C_3], [S_1, 2, 3, 4], [S_2, 1, 1, 2], [S_3, 3, 2, 1]] Using Cramers rule, find the number of cars of each type which can be produced using 29, 13 and 16 tonnes of steel of three types respectively.

The sums of n terms of three arithmetical progressions are S_1, S_2 and S_3dot The first term of each unityand the common differences are 1,2 and 3 respectively. Prove that S_1+S_3=2S_2dot

The sums of n terms of three arithmetical progressions are S_1, S_2 and S_3dot The first term of each unity and the common differences are 1,2 and 3 respectively. Prove that S_1+S_3=2S_2dot

The sums of n terms of three arithmetical progressions are S_1, S_2 and S_3dot The first term of each unity and the common differences are 1,2 and 3 respectively. Prove that S_1+S_3=2S_2dot

Find the product of 7/2s^2t\ a n d\ s+tdot Verify the result for s=1/2a n d\ t=5.