It is currently 09 Apr 2020, 22:38

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A weighted coin has a probability p of showing heads. If suc

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 10225
Followers: 212

Kudos [?]: 2544 [0], given: 9586

A weighted coin has a probability p of showing heads. If suc [#permalink]  01 Dec 2018, 10:54
Expert's post
00:00

Question Stats:

30% (01:47) correct 69% (01:37) wrong based on 33 sessions
A weighted coin has a probability p of showing heads. If successive flips are independent, and the probability of getting at least one head in two flips is greater than 0.5, then what could p be?

Indicate all possible values.

A. 0.1

B. 0.2

C. 0.3

D. 0.4

E. 0.6

F. 0.7
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

VP
Joined: 20 Apr 2016
Posts: 1167
WE: Engineering (Energy and Utilities)
Followers: 19

Kudos [?]: 1096 [3] , given: 234

Re: A weighted coin has a probability p of showing heads. If suc [#permalink]  04 Dec 2018, 06:34
3
KUDOS
Carcass wrote:
A weighted coin has a probability p of showing heads. If successive flips are independent, and the probability of getting at least one head in two flips is greater than 0.5, then what could p be?

Indicate all possible values.

A. 0.1

B. 0.2

C. 0.3

D. 0.4

E. 0.6

F. 0.7

Explanation::

Probability of getting one head = 1 - (probability of no head)

Since the events are independent and there are 2 successive flips,

so,

Let compare each solution:

A) Probability = 0.1 , probability of getting one head = 1 - (1-0.1)^2 = 0.19 (probability of no head = 1 - probability of getting head)
B) Probability = 0.2 , probability of getting one head = 1 - (1-0.2)^2 = 0.36
C) Probability = 0.3 , probability of getting one head = 1 - (1-0.3)^2 = 0.51
D) Probability = 0.4 , probability of getting one head = 1 - (1-0.4)^2 = 0.64
E) Probability = 0.5 , probability of getting one head = 1 - (1-0.5)^2 = 0.75
F) Probability = 0.6 , probability of getting one head = 1 - (1-0.6)^2 = 0.84
G) Probability = 0.7 , probability of getting one head = 1 - (1-0.7)^2 = 0.91

Hence the options are C,D,E,F,G
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Director
Joined: 22 Jun 2019
Posts: 513
Followers: 2

Kudos [?]: 91 [0], given: 157

Re: A weighted coin has a probability p of showing heads. If suc [#permalink]  15 Feb 2020, 11:19
Official Explanation:

Remember that, to calculate the probability of an "at least" scenario, we use the complement rule. The case we want is (at least one H in two flips). The complement of that is (no H in two flips). If p is the probability of H, then (1 – p) is the probability of T. The probability of two T in two flips would be that squared, and then we would subtract from 1 to find the "at least" probability. In the table below, the first column is the possible values of p, the probability of getting H on a single flip. The second column is the probability of getting T on a single flip. The third column is the probability of getting two T's in a row, i.e. no H in two flips; that is the complement of the "at least" case. The final column is the probability of "at least one H in two flips."

Attachment:

Screenshot from 2020-02-16 01-20-29.png [ 86.07 KiB | Viewed 630 times ]

We see that for all value of p ≥ 0.3, the "at least" probability is greater than 0.5.

FAQ: Why is the (1 - p) term being squared?

We know that:

P(tails) = (1 - p)

This problem ultimately asks us to find the probability of getting "at least one heads in two flips". This means that we want to find the probability of getting the following outcomes:

OR
OR

We can calculate all this more easily by first finding the complement to that. The complement to getting "at least one heads in two flips" is getting "exactly 2 tails":

tails, tails

Thus, we're looking for the probability of getting tails AND tails:

P(exactly 2 tails) = P(tails) * P(tails) = P(tails)^2

Substituting in for the value of P(tails), we get:

P(exactly 2 tails) = (1 - p)^2

Taking the complement of this gives us the final expression for our chart:

P(at least one heads) = 1 - P(exactly 2 tails)
P(at least one heads) = 1 - (1 - p)^2

FAQ: Do we really have to make that whole chart? That would take too long!

No, you don't have to fill in that whole chart. That's just being used to illustrate the thinking behind this problem. To solve the problem, you really only need to know that expression in the last column: 1 - (1 - p)^2. We know that that expression must be greater than 0.5. So we end up with:

1 - (1 - p)^2 > 0.5

Now you can just plug in the different answer choices as the value for p in this expression and see which values yield a true statement.
_________________

New to the GRE, and GRE CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides
3rd Party Resource's: All In One Resource's | All Quant Questions Collection | All Verbal Questions Collection | Manhattan 5lb All Questions Collection
Books: All GRE Best Books
Scores: Average GRE Score Required By Universities in the USA
Tests: All Free & Paid Practice Tests | GRE Prep Club Tests
Extra: Permutations, and Combination
Vocab: GRE Vocabulary
FB Group: FB Gre Group

Re: A weighted coin has a probability p of showing heads. If suc   [#permalink] 15 Feb 2020, 11:19
Display posts from previous: Sort by