Gate Exam

If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?

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Gate Other Question

5 skilled workers can build a wall in 20days: 8 semi-skilled workers can build a wall
in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6
semi-skilled and 5 unskilled workers, how long will it take to build the wall?
Four matrices M1, M2, M3 and M4 are dimensions p × q, q × r, r × s and s × t respectively can be multiplied in several ways with different number of total scalar multiplications. For example When multiplied as (( ) ( )) 1 2 3 4 M ×M × M ×M the total number of scalar multiplications is pqr+rst+prt. When multiplied as ((( ) ) ) 1 2 3 4 M ×M ×M ×M , the total number of scalar multiplications is pqr+prs+pst.
If p=10, q=100, r=20, s=5 and t=80, then the minimum number of scalar
multiplications needed is??