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# Everyone who passes the test will be awarded a degree. The p

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Everyone who passes the test will be awarded a degree. The p [#permalink]  24 Apr 2018, 09:33
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Everyone who passes the test will be awarded a degree. The probability that Tom passes the test is 0.5, and the probability that John passes the test is 0.4. The two events are independent of each other.

 Quantity A Quantity B The probability that both Tomand John get the degree The probability that at least oneof them gets the degree

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

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[Reveal] Spoiler: OA

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Re: Everyone who passes the test will be awarded a degree. The p [#permalink]  04 May 2018, 04:14
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I do not think we have to do serious math to answer this question. Both events happening vs any one event happening. B would be greater for obvious reason.

Both events happening = 0.5*0.4 = 0.2

any one event happening = 0.5+0.4 - 0.9

Please correct me on Math part if wrong.
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Re: Everyone who passes the test will be awarded a degree. The p [#permalink]  04 May 2018, 10:25
I could figure out the A answer but I was not so sure of the method for B. Help please?
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Re: Everyone who passes the test will be awarded a degree. The p [#permalink]  07 May 2018, 16:22
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Expert's post
mohan514 wrote:
I do not think we have to do serious math to answer this question. Both events happening vs any one event happening. B would be greater for obvious reason.

Both events happening = 0.5*0.4 = 0.2

any one event happening = 0.5+0.4 - 0.9

Please correct me on Math part if wrong.

kruttikaaggarwal wrote:
I could figure out the A answer but I was not so sure of the method for B. Help please?

So lets see Quantity A: Both get degree = $$P(tom) \times P(john)=0.5 *0.4=0.2$$.

Quantity B: Atleast one degree gets awarded. We can write the following cases:

Tom gets a degree John doesnot = $$0.5 * (1-0.4)=0.3$$

John gets a degree Tom doesnot = $$0.4 * (1-0.5)=0.2$$

Both get a degree = $$0.4 *0.5=0.2$$

Total probability for quantity B is $$0.7$$.

Hence B is greater.
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Re: Everyone who passes the test will be awarded a degree. The p [#permalink]  14 May 2018, 11:42
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Proability that Tom passes the test is 0.5, So, probability that he does not pass the test is also 0.5. and the probability that John passes the test is 0.4. So, the probability that John doesn't pass the test is 0.6. (1-P) equation.

So, probability of both get degree is 0.5*0.4= 0.2.

While probability of both don't get degree is 0.5*0.6 =0.3
Hence, probability of atleast one of them gets degree is (1-0.3) 0.7

Ans. B
Re: Everyone who passes the test will be awarded a degree. The p   [#permalink] 14 May 2018, 11:42
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