10. (4 points) A random committee of size 3 is selected from 4 doctors and 2 nurses. Let X be the random variable repres

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10 4 Points A Random Committee Of Size 3 Is Selected From 4 Doctors And 2 Nurses Let X Be The Random Variable Repres 1 (158.72 KiB) Viewed 13 times

10. (4 points) A random committee of size 3 is selected from 4 doctors and 2 nurses. Let X be the random variable representing the number of doctors on the committee. What is the value of P(2 ≤X ≤3) ? O 7/9 O 7/10 O 5/6 O 2/3 O 3/5 O 7/12 8/15 ✓ 4/5 11. A computer algorithm takes an integer from a specified range at random and tests whether the selected integer is a prime number using the known methods. If the integer is a prime number, the algorithm halts and outputs the prime number. Otherwise, it repeats the same cycle by selecting again an integer from the specified range. The probability of being a prime number in the specified range is 0, 0237. (a) (1 point (bonus)) What is the expected number of trials till the computer algorithm halts? 40.194092827 O 41.194092827 O 45.194092827 43.194092827 39.194092827 ✓42.194092827 O 44.194092827 O 38.194092827 (b) (2 points (bonus)) What is the probability that the number of integers that are tested is at most 10 when the algorithm halts? O 0.2232569898 0.2032569898 O 0.1932569898 ✓ 0.2132569898 O 0.2332569898 O 0.1832569898 O 0.2432569898 O 0.2532569898 12. (2 points (bonus)) The lifetime of specific type of machines in years is modelled by the Weibull distribution T. The probability density function of T is defined as b-1 b (t - 1 (1) ¹ (1)², 120. a a w(t) = If the parameters are a = 1.72 and = 0.86, for a randomly selected machine, what would be the probability that its lifetime is greater than 3 years? 0.239188605 ✓0.199188605 O 0.219188605 0.179188605 O 0.169188605 O 0.209188605 O 0.229188605 O 0.189188605