Question

x plays y at table tennis and from past experience wins 3 sets in every 5 played. if they play 6 sets, write down the probability generator and hence determine the probability that a. y wins 3 of them b. Y wins at least 5 of them.

Answer 1

The probability x win a set is 3 in 5, 0.6.

The probability that x wins m sets from a total of N is given by the formula:

$P(MX|N)=\frac{N!}{M!(N-M)!}\cdot0.6^M0.4^{N-M}$

a) If they play 6 sets, the probability that y wins 3 of then is given by:

$P(3X|6)=\frac{6!}{3!3!}\cdot0.6^3\cdot0.4^3=0.276$

b) The probability that y wins at least 5 of then is given by:

$P(1X|6)+P(0X|6)=6\cdot0.4^5\cdot0.6+0.4^6=0.041$