Question

1)    Events A, B, C, and D are mutually exclusive and collectively exhaustive. If P(A or B) = .44. Circle all of the following that are possible?

       a)    P(C or D) > .56

       b)    P(C and D) = .56

       c)    P(A and D) = 0

       d)    P(A) = .5

2)    You have 10 members of a team. How many ways could you pick 3 captains (order does not matter)?

       a)    720

       b)    30

       c)    120

       d)    None of the above

4)    What is the mean of the following probability distribution (you must solve for the missing probability)?

            X         |           P(X)

            10        |           .5

            20        |           .3

            30        |           .1

            40        |           ?

            a)         14

            b)         18

            c)         30

            d)         None of the above

5)      For two independent observations from a random variable with normal probability distribution with a mean of 27 and standard deviation of 3, what is the probability that you will get value greater than 27 in your first observation and a value less than 21 in your second observation?

          a)      .2500

          b)     .5228

          c)      .2386

          d)     .0114

Answer 1

TOPIC: 1.Probability,

2.Combinatorics,

3.Expected value of a random variable,

4.Use of Normal distribution to find the required probabilities.

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(2) P (A on B) 0.44 A and B are aao ? P (A) +P (B) 0.44. events ヲ P (B) = o, 44 ← P (A) Nour, 항, 꾸(A)=0.5 ; then, _ w hich Hence, ④ is done ont So, the corneet answer isop tion- P (A and D) -o ate to mem bers in the team. Thes 3 captains ender daes not matte, can be chasen in (3) There aure 2 So, peuined o. 129

iven thepob P (X 0.5 0.3 0. 1 lO 20 140 Now, since, p (x) is a、 pmt; they we must haw 0.5 +0.3 + 0-1+a The m x reduces to - lO 20.3 30 | 0.1 Total10 E (X) mean (x) χ, p (x) !' OL