) Your younger cousin Jack plays hockey and you attend their game. Jack likes to be the goalkeeper, but it depends on who his coach is that day. Coach Alex prefers Jack to not be goalkeeper and will assign Jack to be a goalkeeper with 0.3 probability. Coach Tom will assign Jack to be a goalkeeper 50% of the time. Coach Tom is the main coach attending 8 out of 10 games. b. What is the probability that Jack will be a goalkeeper? Use 2 decimals. (c. You show up late and don’t see the coach, but Jack is the goalkeeper. What is the probability that Alex is coaching given Jack is a goalkeeper? Use 4 decimals. d. What is the probability that Jack is a goalkeeper or the coach is Tom?
b)
| P(Jack is goalkeeper)=P(Tom)*P(Jack is goalkeeper|Tom)+P(Alex)*P(Jack is goalkeeper|Alex) | ||||||
| =0.8*0.5+0.2*0.3=0.46 | ||||||
c)
| P(Alex|Jack is goalkeeper)=P(Alex)*P(Jack is goalkeeper|Alex)/P(Jack is goalkeeper)=0.2*0.3/0.46 =0.1304 |
d)
probability that Jack is a goalkeeper or the coach is Tom =P(goal keeper)+P(Tom )-P(both)
=0.46+0.8-0.8*0.5
=0.86
) Your younger cousin Jack plays hockey and you attend their game. Jack likes to be...
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