The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.35. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?  Options
A) A)0.8321  B) B)0.7  C) C)0.895  D) D)0.7531  E) E)0.8213
Out of 100 matches:   Matt is plays in 80 and not plays in 20.   Out of 80 matches Matt plays in, team wins   0.75*80= 
<gadget id="calculator">  0.75*80</gadget>
<output>60</output>
60.   Out of 20 matches Matt does not play in, team wins   0.35*20= 
<gadget id="calculator">  0.35*20</gadget>
<output>7</output>
7.   So, out of 100 matches 60 + 7= 
<gadget id="calculator">60 + 7</gadget>
<output>67</output>
67 are won.   It is known that the team has won the last match. Out of 67 matches won, Matt is in 60: 60/67= 0.895...   Answer: 0.895.
<result>C</result>
The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.35. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?