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Probability and Problem Solving

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Probability and Problem Solving  [#permalink]

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New post 16 Feb 2020, 20:15
The probability of Alice hitting the target while shooting is 0.4 and probability of either Alice, Ban or both hitting the target is 0.8.
I) What is the probability of Ban hitting the target, if both events are mutually exclusive?
II) What is the probability of Ban hitting the target, if both events are independent?

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Re: Probability and Problem Solving  [#permalink]

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New post 16 Feb 2020, 22:58
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sark19 wrote:
The probability of Alice hitting the target while shooting is 0.4 and probability of either Alice, Ban or both hitting the target is 0.8.
I) What is the probability of Ban hitting the target, if both events are mutually exclusive?
II) What is the probability of Ban hitting the target, if both events are independent?

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if mutually exclusive:
we can put it in the table shown.
we can't find B because of insufficient info

if independent:
\(A = 0.4\)
\(A∪B = A + B - A∩B = 0.8\)
\(A∩B= A*B = 0.4B\)

\(B - 0.4B = 0.4\)
\(0.6B = 0.4\)
\(B = \frac{2}{3}\)
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Re: Probability and Problem Solving  [#permalink]

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New post 17 Feb 2020, 05:05
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MahmoudFawzy, what basically the equation will be as follows

if mutually exclusive:

P(the target is hit) = P(A)P(B')+P(B)P(A')
as we don't know P(B), we cant determine the answer
am i correct?
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Probability and Problem Solving  [#permalink]

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New post 17 Feb 2020, 05:43
Hi, Kindly repost the question according to the rules: https://gmatclub.com/forum/rules-for-po ... 33935.html

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Re: Probability and Problem Solving  [#permalink]

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New post 17 Feb 2020, 16:37
J2S2019 wrote:
MahmoudFawzy, what basically the equation will be as follows

if mutually exclusive:

P(the target is hit) = P(A)P(B')+P(B)P(A')
as we don't know P(B), we cant determine the answer
am i correct?


For Independent or Exclusive, the same equation applies:
P(hit) = P(A)(B) + P(A)(B') + P(B)(A')

The difference is in calculating P(A)(B) and P(A')(B'), which can be calculated by multiplication in case of independent but not in Exclusive.
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Re: Probability and Problem Solving  [#permalink]

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New post 18 Feb 2020, 11:27
sark19 wrote:
The probability of Alice hitting the target while shooting is 0.4 and probability of either Alice, Ban or both hitting the target is 0.8.
I) What is the probability of Ban hitting the target, if both events are mutually exclusive?
II) What is the probability of Ban hitting the target, if both events are independent?

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I) What is the probability of Ban hitting the target, if both events are mutually exclusive?
Mutually exclusive—> P(A&B) = 0
—> P(A) + P(B) - P(A&B) = 0.8
—> 0.4 + P(B) - 0 = 0.8
—> P(B) = 0.4
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Re: Probability and Problem Solving   [#permalink] 18 Feb 2020, 11:27
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