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Lin and Mark each attempt independently to decode a message.

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Lin and Mark each attempt independently to decode a message. [#permalink] New post 31 May 2019, 09:32
Expert's post
Lin and Mark each attempt independently to decode a message. If the probability that Lin will decode the message is 0.80 and the probability that Mark will decode the message is 0.70, find the probability that

(a) both will decode the message
(b) at least one of them will decode the message
(c) neither of them will decode the message

[Reveal] Spoiler: OA
(a) 0.56 (b) 0.94 (c) 0.06


Math Review
Question: 15
Page: 298
Difficulty: medium

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Re: Lin and Mark each attempt independently to decode a message. [#permalink] New post 31 May 2019, 10:09
Expert's post
Carcass wrote:
Lin and Mark each attempt independently to decode a message. If the probability that Lin will decode the message is 0.80 and the probability that Mark will decode the message is 0.70, find the probability that

(a) both will decode the message
(b) at least one of them will decode the message
(c) neither of them will decode the message

ASIDE:
If P(Lin decodes message) = 0.8, then P(Lin DOESN'T decode message) = 0.2
If P(Mark decodes message) = 0.7, then P(Mark DOESN'T decode message) = 0.3


[Reveal] Spoiler: OA
(a) 0.56 (b) 0.94 (c) 0.06


Math Review
Question: 15
Page: 298
Difficulty: medium


(a) both will decode the message
P(BOTH decode message) = P(Lin decodes message AND Mark decodes message)
= P(Lin decodes message) x P(Mark decodes message)
= 0.80 x 0.70
= 0.56

Answer: 0.56
------------------------------------------

(b) at least one of them will decode the message
We want P(at least 1 person decodes message)
When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)

So, here we get: P(at least 1 person decodes) = 1 - P(not having at least 1 person decodes)
What does it mean to not have at least 1 person decode? It means getting ZERO decodes.

So, we can write: P(at least 1 person decodes message) = 1 - P(ZERO people decode)

Let's calculate P(ZERO people decode)

P(ZERO people decode) = P(Lin does NOT decode AND Mark does NOT decode)
= P(Lin does NOT decode) x P(Mark does NOT decode)
= 0.2 x 0.3
= 0.06

So, P(at least 1 person decodes message) = 1 - 0.06
= 0.94

Answer: 0.94
------------------------------------------

(c) neither of them will decode the message
P(neither person decodes message) = P(Lin does NOT decode AND Mark does NOT decode)
= P(Lin does NOT decode) x P(Mark does NOT decode)
= 0.2 x 0.3
= 0.06

Answer: 0.06

Cheers,
Brent
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Re: Lin and Mark each attempt independently to decode a message.   [#permalink] 31 May 2019, 10:09
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