Answer to Question #188560 in Statistics and Probability for LE8

Question

Akali made a bet to Kai'Sa wherein in 7 throws, Seraphine will hit the bull's eye once, 3 triples, 3 doubles, and no misses.

Seraphine's stats are as follows,

0.09 for bull's eye, 0.22 for triples, 0.34 for doubles, and 0.03 for a complete miss.

What is the probability of Akali's prediction?

Answer (decimal form, 4 decimal places)

Answer 1

By condition,

${p_1} = 0.09,\,\,{p_2} = 0.22,\,\,{p_3} = 0.34, p_4=0.03$

Using the polynomial scheme, we find the probability of Alakali prediction that in 7 throws, Seraphine will hit the bull's eye once, 3 triples, 3 doubles, and no misses.

$P(4,3,2,1) = \dfrac{{7!}}{{4!3!2!1!}}p_1^3p_2^2{p_3}^2p_4^2 = \dfrac{35}{2}(0.09)^2(0.22)^2(0.34)^2(0.03)^2=0.00728$

Answer: P=0.00728