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

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GRE Prep Club Legend
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Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 117

Kudos [?]: 1895 [0], given: 397

The probability is that a certain coin will turn up heads on [#permalink] New post 30 Jul 2018, 10:42
Expert's post
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Question Stats:

94% (00:23) correct 5% (00:34) wrong based on 17 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
GRE Prep Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 117

Kudos [?]: 1895 [0], given: 397

Re: The probability is that a certain coin will turn up heads on [#permalink] New post 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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The probability is that a certain coin will turn up heads on

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