Question

Zambian soccer team wins (W) with probability 0.6, loses (L) with probability 0.3 and ties with probability 0.1. The team plays three games over the weekend. What is the probability that

(i) The team wins at least twice and does not lose? (3 marks)

(ii) The team wins, loses and ties?

Answer 1

$$WWW, WWL, WWT, WLW, WTW, LWW,$$

$$TWW,WLL, WLT, WTL, WTT, LWL,$$

$$LWT, TWL, TWT, LLW, LTW, TLW,$$

$$TTW,LLL, LLT, LTL, TLL, LTT,$$

$$TLT,TTL, TTT$$

There are $3^3=27$ outcomes.

(i) the probability that the team wins at least twice and does not lose?

$$WWW, WWT, WTW, TWW$$

$$p=\dfrac{4}{27}$$

(i) the probability that the team wins, loses and ties

$$WLT, WTL,LWT, TWL, LTW, TLW$$

$$p=\dfrac{6}{27}=\dfrac{2}{9}$$