Probability question

  • #1

Homework Statement


Two hockey players, Wayne and Mario, each independently take a penalty shot. Wayne has a 7/10 chance of scoring, while Mario has a 3/5 chance of scoring. What is the probability that;

a) they both miss


Homework Equations


P(A and B) = P(A) x P(B)


The Attempt at a Solution


For this question I found out what the complements (P(not mario) and P(not Wayne)) for each were and then I used the formula for independent events [P(A and B) = P(A) x P(B)] to find my answer and the answer that I got was correct. However, I was wondering why I cannot just go:

P(both miss) = 1- P(both score)

I tried this method and the answer that came up was different than the answer that I got from my first method of trying to solve this question (using the complements). Could someone explain why I cannot use "P(both miss) = 1- P(both score)" to solve this question?
 

Answers and Replies

  • #2
danago
Gold Member
1,122
4

Homework Statement


Two hockey players, Wayne and Mario, each independently take a penalty shot. Wayne has a 7/10 chance of scoring, while Mario has a 3/5 chance of scoring. What is the probability that;

a) they both miss


Homework Equations


P(A and B) = P(A) x P(B)


The Attempt at a Solution


For this question I found out what the complements (P(not mario) and P(not Wayne)) for each were and then I used the formula for independent events [P(A and B) = P(A) x P(B)] to find my answer and the answer that I got was correct. However, I was wondering why I cannot just go:

P(both miss) = 1- P(both score)

I tried this method and the answer that came up was different than the answer that I got from my first method of trying to solve this question (using the complements). Could someone explain why I cannot use "P(both miss) = 1- P(both score)" to solve this question?

P(both score) is the probability that both mario AND wayne score. The complement of P(both) is the probability that not both of them score, so it could mean that one of them scores and the other doesnt, not necessarily that they both miss.

i.e.
[tex]
1-P(A \cap B) = P(\overline{A\cap B}) \neq P(\overline{A} \cap \overline{B})
[/tex]
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,847
967
1 - P(A)(P(B) is "1- probability they both score" and so is probability the do not BOTH score. But "not both scoring" is not the same as "both do not score". "Not both scoring" includes one scores and the other does not.
 

Related Threads on Probability question

  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
4
Views
986
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
12
Views
1K
Top