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# The probability is that a certain coin will turn up heads on

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Joined: 07 Jun 2014
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The probability is that a certain coin will turn up heads on [#permalink]  30 Jul 2018, 10:42
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Question Stats:

92% (00:24) correct 7% (00:34) wrong based on 14 sessions
The probability is $$\frac{1}{2}$$ that a certain coin will turn up heads on any given toss and the probability is $$\frac{1}{6}$$ that a number cube with faces numbered 1 to 6 will turn up any particular number. What is the probability of turning up a heads and a 6?

A. $$\frac{1}{36}$$
B. $$\frac{1}{12}$$
C. $$\frac{1}{6}$$
D. $$\frac{1}{4}$$
E. $$\frac{2}{3}$$
[Reveal] Spoiler: OA

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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1741 [0], given: 397

Re: The probability is that a certain coin will turn up heads on [#permalink]  07 Aug 2018, 06:04
Expert's post
Explanation

The probability of independent events A and B occurring is equal to the product of the probability of event A and the probability of event B.

In this case, the probability of the coin turning up heads is $$\frac{1}{2}$$ and the probability of rolling a 6 is $$\frac{1}{6}$$. Therefore, the probability of heads and a 6 is equal to $$\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}$$.

Alternatively, list all the possible outcomes: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6.

There are 12 total outcomes and only 1 with heads and a 6. Therefore, the desired outcome divided by the total number of outcomes is equal to $$\frac{1}{12}$$.
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Sandy
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Re: The probability is that a certain coin will turn up heads on   [#permalink] 07 Aug 2018, 06:04
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