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# If the probability that the first event will occur is , and

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Joined: 07 Jun 2014
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If the probability that the first event will occur is , and [#permalink]  24 Nov 2017, 20:52
Expert's post
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Question Stats:

85% (01:48) correct 14% (01:19) wrong based on 14 sessions
If the probability that the first event will occur is $$\frac{1}{4}$$, and the probability that the second event will occur is $$1 \div \sqrt{x+2}$$, then what is the probability that both events will occur?

A. $$\sqrt{x+2} \div (4x + 8)$$
B. $$\sqrt{x+2} \div 4$$
C. $$\sqrt{x+2} \div (16x + 32)$$
D. $$4 \div \sqrt{x+2}$$
E. $$4 \times \sqrt{x+2}$$

Drill 2
Question: 3
Page: 524
[Reveal] Spoiler: OA

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Re: If the probability that the first event will occur is , and [#permalink]  02 Dec 2017, 07:36
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sandy wrote:
If the probability that the first event will occur is $$\frac{1}{4}$$, and the probability that the second event will occur is $$1 \div \sqrt{x+2}$$, then what is the probability that both events will occur?

A. $$\sqrt{x+2} \div (4x + 8)$$
B. $$\sqrt{x+2} \div 4$$
C. $$\sqrt{x+2} \div (16x + 32)$$
D. $$4 \div \sqrt{x+2}$$
E. $$4 \times \sqrt{x+2}$$

Drill 2
Question: 3
Page: 524

The event occuring together P(A and B) = P(A) * P (B)

here we write as p($$\frac{1}{4}$$ and $$1 \div \sqrt{x+2}$$ ) = $$\frac{1}{4}$$ * $$\frac{1}{{\sqrt{x+2}}}$$

or we can write as = $$\frac{1}{4}$$ * $$\frac{1}{{\sqrt{x+2}}}$$ * $${\sqrt{x+2}}\div{\sqrt{x+2}}$$

or we can write as = $$\sqrt{x+2} \div (4x + 8)$$ (since 4 * $$\sqrt{x+2} * \sqrt{x+2}$$ = 4x + 8 )
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1776 [0], given: 397

Re: If the probability that the first event will occur is , and [#permalink]  29 Dec 2017, 13:17
Expert's post
Explanation

Plug In to make this problem much simpler. If you plug in x = 2, then the probability for the second event is: $$1 \div \sqrt{4}=\frac{1}{2}$$.

Now, because this is an “and” probability problem, you multiply the two probabilities together to find the target answer:

$$\frac{1}{4}\times \frac{1}{2}=\frac{1}{8}$$.

Choice A is the only one that works.
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Re: If the probability that the first event will occur is , and   [#permalink] 29 Dec 2017, 13:17
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