Question

1. A fair coin is tossed ten times. (a) What is the probability that all ten tosses produce the small result? (b) What is the probability that the results alternate, i,e., Tail is followed by Head and head is followed by Tail? (c) What is the probability that the first five tosses produce identical results?

2. A point M is chosen in random within the unit square . (a) What is the probability that M is closer to Y- axis than to X- axis? (b) If M is known to be closer to Y - axis than to X,- axis what is the probability that it is closer to point Z (1,1) than to X- axis? please draw the X-axis and Y - axis , put a point Z (1,1) and M is a random number is in the between of X,Y -axis.

3. In the processing board, there is an important component ( A) whose failure is likely going to result in the failure of the board. Specifically, if A fails, board will fail with the probability of 90%. on the other hand, if A is operational, board fails with the probability of 5%. Assume A fails with probability of 10%.

(a) Find the probability of the board's failure.

(b) What is the probability that an observed board's failure has been caused by the failure of A ?

Answer 1