Question

Ten artists (of two different experience levels) are exhibiting their paintings in an art gallery. Three have exhibited in previous shows (making them “experienced artists”) and seven have not. If a patron selects three paintings to purchase at random, find the probability of selecting:

(A) the probability of selecting at least 2 experienced artists’ paintings.

(B) the probability of selecting no experienced artists’ paintings.

(C) the probability of selecting some experienced artists’ paintings.

(D) the probability of selecting less than 2 experienced artists’ paintings.

Answer 1

P (selecting experienced artists' painting") = B = + (say) patron selects 3 paintings Now a random. let Х be selected random variable denoting number of experienced antists' paintings out of 3 paintings by the patron : xn Binomial ( 3 , p = 3 ) A) Probability of selecting at least experienced artists' paintings = P( x2) (3) (3) (5) 3x (0.3) (0.7) + (0.3) 2 3 +(3) (. 3 0.216. B) Probability of selecting no experienced artists' paintings P(x=0) 3 10.7) = 01343 () (7) (7)

c) Probability of selecting some experienced artists' paintings = P(x²1) = 1- P(x=0) 1- 0.343 = 0.65 7. ress than 2 Probability of selecting artists' paintings experienced = P ( x<2) = P(x <1) = P(x=0) + P(x = 1) (3) (7) (7.) + (3) 1) (7) (17)3 + 3 (0:3) (0.7) ² 0.343 0.441 0.784 .