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# A consignment of eight washing machines contains two fully-automatic

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Joined: 02 Sep 2009
Posts: 51121
A consignment of eight washing machines contains two fully-automatic  [#permalink]

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02 Oct 2018, 01:32
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Difficulty:

25% (medium)

Question Stats:

74% (01:42) correct 26% (01:27) wrong based on 34 sessions

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A consignment of eight washing machines contains two fully-automatic washing machines and six semi-automatic washing machines. If two washing machines are to be chosen at random from this consignment, what is the probability that at least one of the two washing machines chosen will be a fully-automatic?

(A) 1/5

(B) 1/4

(C) 3/14

(D) 13/28

(E) 17/28

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A consignment of eight washing machines contains two fully-automatic  [#permalink]

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02 Oct 2018, 04:22
Bunuel wrote:
A consignment of eight washing machines contains two fully-automatic washing machines and six semi-automatic washing machines. If two washing machines are to be chosen at random from this consignment, what is the probability that at least one of the two washing machines chosen will be a fully-automatic?

(A) 1/5

(B) 1/4

(C) 3/14

(D) 13/28

(E) 17/28

There are $$C_2^8 = 28$$ ways of choosing 2 from the 8 washing machines available. Of the 8
machines, we have 2 fully-automatic washing machines and 6 semi-automatic machines.

P(at least one is fully-automatic) = 1 - P(Both are semi-automatic machines)

There are $$C_2^6 = 15$$ ways of choosing 2 from 6 semi-automatic washing machines.

P(Both are semi-automatic machines) = $$\frac{15}{28}$$ | P(at least one is fully automatic) = $$1 - \frac{15}{28} = \frac{13}{28}$$

Therefore, the probability that at least one of the two washing machines chosen will be a fully-automatic is $$\frac{13}{28}$$ (Option D)
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Re: A consignment of eight washing machines contains two fully-automatic  [#permalink]

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02 Oct 2018, 04:34
Bunuel wrote:
A consignment of eight washing machines contains two fully-automatic washing machines and six semi-automatic washing machines. If two washing machines are to be chosen at random from this consignment, what is the probability that at least one of the two washing machines chosen will be a fully-automatic?

(A) 1/5

(B) 1/4

(C) 3/14

(D) 13/28

(E) 17/28

Probability of ATLEAST 1 event : P(AT LEAST 1)
Probability of NO EVENT: P(NONE)

P(AT LEAST 1) = 1 - P(NONE)

P(NONE): Both washing machines are semiautomatic (one AND two, both are semi)

P(NONE): P1 (Probability of choosing 1st Washing machine) X P2 (Probability of choosing 1st Washing machine)

P(NONE): 6/8 X 5/7 .........................As 6 ways to choose first washing machine and after first is chosen, 5 ways to choose second one

P(NONE): 13/28

P(AT LEAST 1) = 1 - 15/28

= 13/28

= D
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Re: A consignment of eight washing machines contains two fully-automatic &nbs [#permalink] 02 Oct 2018, 04:34
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# A consignment of eight washing machines contains two fully-automatic

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