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# M17-36

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Math Expert
Joined: 02 Sep 2009
Posts: 42355

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16 Sep 2014, 01:02
00:00

Difficulty:

5% (low)

Question Stats:

95% (00:53) correct 5% (01:37) wrong based on 112 sessions

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The probability that event A will occur is 20%. If event A occurs, the probability that event B will occur is 30%. What is the probability that event A will occur but event B will not?

A. $$\frac{1}{10}$$
B. $$\frac{7}{55}$$
C. $$\frac{5}{36}$$
D. $$\frac{7}{50}$$
E. $$\frac{5}{24}$$
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 42355

Kudos [?]: 133182 [0], given: 12439

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16 Sep 2014, 01:02
Official Solution:

The probability that event A will occur is 20%. If event A occurs, the probability that event B will occur is 30%. What is the probability that event A will occur but event B will not?

A. $$\frac{1}{10}$$
B. $$\frac{7}{55}$$
C. $$\frac{5}{36}$$
D. $$\frac{7}{50}$$
E. $$\frac{5}{24}$$

The probability that event A will occur but event B will not = (the probability that event A will occur)*(1 - the probability that event B will occur) = $$\frac{1}{5}(1 - 0.3) = \frac{1}{5}*\frac{7}{10} = \frac{7}{50}$$.

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03 Nov 2014, 07:36
Bunuel wrote:
Official Solution:

The probability that event A will occur is 20%. If event A occurs, the probability that event B will occur is 30%. What is the probability that event A will occur but event B will not?

A. $$\frac{1}{10}$$
B. $$\frac{7}{55}$$
C. $$\frac{5}{36}$$
D. $$\frac{7}{50}$$
E. $$\frac{5}{24}$$

The probability that event A will occur but event B will not = (the probability that event A will occur)*(1 - the probability that event B will occur) = $$\frac{1}{5}(1 - 0.3) = \frac{1}{5}*\frac{7}{10} = \frac{7}{50}$$.

IS this not a case of conditional probability???????

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Intern
Joined: 09 Jul 2016
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20 May 2017, 04:12
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Will the cases change if the events are not mutually exclusive?

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20 May 2017, 05:32
Vikram_Katti wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Will the cases change if the events are not mutually exclusive?

Could you elaborate your case? If the conditionals change, the result will change.
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30 May 2017, 06:45
We need to find the probability that event B does not occur given that event A occurs. Probability of A occurring is 0.2 and probability of B not occurring is 0.7. Hence the required probability is 0.7*0.2=0.14 or 14/100 or 7/50. Hence option D.
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31 May 2017, 23:12
probability of A=1/5
probability that B will not occur=1-3/10=7/10
hence probability =1/5*7/10=7/50

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Manager
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08 Sep 2017, 22:36
I find a matrix makes this problem a bit more digestible.
>> !!!

You do not have the required permissions to view the files attached to this post.

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13 Nov 2017, 23:03
Bunuel wrote:
The probability that event A will occur is 20%. If event A occurs, the probability that event B will occur is 30%. What is the probability that event A will occur but event B will not?

A. $$\frac{1}{10}$$
B. $$\frac{7}{55}$$
C. $$\frac{5}{36}$$
D. $$\frac{7}{50}$$
E. $$\frac{5}{24}$$

Bunuel, if I change the question :

From If event A occurs, the probability that event B will occur is 30%
To The probability that event B will occur is 30% (I eliminate "If event A occurs")

Do we have the same answer?

Thank you
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14 Nov 2017, 04:18
septwibowo wrote:
Bunuel wrote:
The probability that event A will occur is 20%. If event A occurs, the probability that event B will occur is 30%. What is the probability that event A will occur but event B will not?

A. $$\frac{1}{10}$$
B. $$\frac{7}{55}$$
C. $$\frac{5}{36}$$
D. $$\frac{7}{50}$$
E. $$\frac{5}{24}$$

Bunuel, if I change the question :

From If event A occurs, the probability that event B will occur is 30%
To The probability that event B will occur is 30% (I eliminate "If event A occurs")

Do we have the same answer?

Thank you

If the events are independent, then yes.
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Re: M17-36   [#permalink] 14 Nov 2017, 04:18
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# M17-36

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