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If the probability of Sita getting selected to a school...

by BTGmoderatorLU » Sun Jan 21, 2018 7:59 am
If the probability of Sita getting selected to a school is 20% and she applied to 3 schools. What is the probability that she will get selected in at least one school?

A. 24/125
B. 21/125
C. 61/125
D. 12/125
E. 18/125

The OA is C.

I'm confused with this PS question. Experts, any suggestion about how to solve? I don't understand this question. Thanks in advance.
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by [email protected] » Sun Jan 21, 2018 10:50 am
Hi LUANDATO,

We're told that the probability of Sita getting selected to any individual school is 20% and that she applied to 3 schools. We're asked for the probability that she will get selected to AT LEAST one school.

With these types of probability questions, it's often easiest to calculate the probability of what you DON'T WANT - and then subtract that fraction from 1 to determine the probability of what you DO want. The question asks for the probability that she will get selected to AT LEAST one school, so we'll calculate the probability that she will get selected to 0 schools. A 20% chance of getting selected means an 80% chance of NOT getting selected. Since the answers are fractions, we should write 80% as 4/5:

(Not selected)(Not selected)(Not selected) = (4/5)(4/5)(4/5) = 64/125 chance of getting selected by 0 schools

Thus, he probability that she will get selected to AT LEAST one school is... 1 - 64/125 = 61/125

Final Answer: C

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by EconomistGMATTutor » Sun Jan 21, 2018 11:47 am
If the probability of Sita getting selected to a school is 20% and she applied to 3 schools. What is the probability that she will get selected in at least one school?

A. 24/125
B. 21/125
C. 61/125
D. 12/125
E. 18/125

The OA is C.

I'm confused with this PS question. Experts, any suggestion about how to solve? I don't understand this question. Thanks in advance.
Hi LUANDATO,
Let's take a look at your question.

The probability of Sita getting selected to a school = 20% = 20/100 = 1/5
This question can easily be solved by calculating the probability of opposite event.
The probability of Sita not getting selected to a school = 1 - 1/5 = 4/5

Probability that Sita not getting selected at all three schools can be calculated as:
$$=\left(\frac{4}{5}\right)^3=\frac{65}{125}$$

Now we can solve the probability of Sita getting selected in atleast one school as:
$$=1-\frac{64}{125}=\frac{125-64}{125}=\frac{61}{125}$$

Therefore, Option C is correct.

Hope it helps.
I am available if you's like any follow up.
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by Jeff@TargetTestPrep » Tue Jan 23, 2018 9:11 am
LUANDATO wrote:If the probability of Sita getting selected to a school is 20% and she applied to 3 schools. What is the probability that she will get selected in at least one school?

A. 24/125
B. 21/125
C. 61/125
D. 12/125
E. 18/125
We can use the equation:

P(selected into at least 1 school) = 1 - P(selected to no schools)

P(selected to no schools) = 4/5 x 4/5 x 4/5 = 64/125

Thus,

P(selected into at least 1 school) = 1 - 64/125 = 61/125

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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