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) =

0.2If P(Mark decodes message) = 0.7, then P(Mark DOESN'T decode message) =

0.3(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= 0.06So, P(at least 1 person decodes message) = 1 -

0.06= 0.94

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

(c) neither of them will decode the messageP(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: 0.06Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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