Question

A certain player, say $X$, known to win with probability $0.3$ if the track is fast and $0.4$ if the track is slow. For Monday, there is a $0.7$ probability of a fast track and $0.3$ probability of a slow track. The probability that player $X$ will win a Monday, is

• A. $0.22$
• B. $0.11$
• C. $0.33$
• D. None of these

Answer 1

The correct option is C $0.33$

Let us define the events:
$W:$ Players wins on Monday
$F:$ Track is fast
$S:$ Track is slow
We have given: $P\left(F\right)=0.7,P\left(S\right)=0.3,P\left(\frac{W}{F}\right)=0.3,P\left(\frac{W}{S}\right)=0.4$
$\therefore P($ player $X$ will win on Monday $)$
$=P\left(W\right)=P(W\cap F)+P(W\cap S)=P\left(F\right)\times P\left(\frac{W}{F}\right)+P\left(S\right)\times P\left(\frac{W}{S}\right)=0.7\times 0.3+0.3\times 0.4=0.33$