Last visit was: 20 Jul 2024, 14:31 It is currently 20 Jul 2024, 14:31
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# A fair coin is to be tossed twice and an integer is to be

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 18 Mar 2012
Posts: 38
Own Kudos [?]: 1184 [29]
Given Kudos: 117
GPA: 3.7
Math Expert
Joined: 02 Sep 2009
Posts: 94431
Own Kudos [?]: 642557 [10]
Given Kudos: 86710
General Discussion
Manager
Joined: 24 Sep 2012
Posts: 67
Own Kudos [?]: 412 [0]
Given Kudos: 3
Location: United States
GMAT 1: 730 Q50 V39
GPA: 3.2
WE:Education (Education)
Intern
Joined: 17 Apr 2013
Posts: 49
Own Kudos [?]: 331 [0]
Given Kudos: 298
Location: United States
Concentration: Other, Finance
Schools: SDSU '16
GMAT 1: 660 Q47 V34
GPA: 2.76
WE:Analyst (Real Estate)
Re: A fair coin is to be tossed twice and an integer is to be [#permalink]
alex1233 wrote:
A fair coin is to be tossed twice and an integer is to be selected at random from one of the integers 3, 8, and 10. What is the probability that at least one head is tossed and an even integer is selected?

A. 1/6
B. 1/4
C. 1/3
D. 1/2
E. 7/12

Hi all,

I'm not quiet sure whether my reasoning is correct or not
I assumed two cases :
1) 1 head + 1 even = 1/2 * 2/3 = 2/6
2) 2 heads + 1 even = 1/2 * 1/2 * 2/3 = 1/6
did get the result by luck ?

Thx
Math Expert
Joined: 02 Sep 2009
Posts: 94431
Own Kudos [?]: 642557 [0]
Given Kudos: 86710
Re: A fair coin is to be tossed twice and an integer is to be [#permalink]
clipea12 wrote:
alex1233 wrote:
A fair coin is to be tossed twice and an integer is to be selected at random from one of the integers 3, 8, and 10. What is the probability that at least one head is tossed and an even integer is selected?

A. 1/6
B. 1/4
C. 1/3
D. 1/2
E. 7/12

Hi all,

I'm not quiet sure whether my reasoning is correct or not
I assumed two cases :
1) 1 head + 1 even = 1/2 * 2/3 = 2/6
2) 2 heads + 1 even = 1/2 * 1/2 * 2/3 = 1/6
did get the result by luck ?

Thx

We are told that a coin is to be tossed twice. So, the case with one head means 1 head and 1 tail. So, if you do this way it should be:

1. P(head, tail) * P(even) = (2*1/2*1/2)*2/3 = 2/6. We should multiply 1/2*1/2 by 2, because HT can occur in two ways HT and TH.

Overall = 2/6 + 1/6.
Intern
Joined: 11 Jun 2014
Posts: 43
Own Kudos [?]: 70 [0]
Given Kudos: 3
Concentration: Technology, Marketing
GMAT 1: 770 Q50 V45
WE:Information Technology (Consulting)
Re: A fair coin is to be tossed twice and an integer is to be [#permalink]
This is actually quite simple.

first part
a coin is tossed twice.
so probability of at least 1 head = 1 - P( all tails)
P(at least 1 head) = 1 - {(1/2)*(1/2)}
= 1 - (1/4) = 3/4

second part
there are 3 integers out of which 2 are even,
P( even integer ) = 2/3

so P( at least 1 head and 1 even integer) = (3/4) * (2/3) = 2/4 = 1/2

Ans D
Tutor
Joined: 20 Aug 2015
Posts: 349
Own Kudos [?]: 1409 [0]
Given Kudos: 10
Location: India
GMAT 1: 760 Q50 V44
Re: A fair coin is to be tossed twice and an integer is to be [#permalink]
alex1233 wrote:
A fair coin is to be tossed twice and an integer is to be selected at random from one of the integers 3, 8, and 10. What is the probability that at least one head is tossed and an even integer is selected?

A. 1/6
B. 1/4
C. 1/3
D. 1/2
E. 7/12

This questions can teach us two things:
1. Use the negation method in the at least questions. Subtract the probaility of undesired cases from 1 to get the probability of desired cases. It is almost always easier to solve.
2. If the question uses "AND" in between two probabilities, we need to multiply the probabilities

Probability of at least one head = 1 - P(0 Heads) = 1 - 1/4 = 3/4
We have the following cases : HH, HT, TH and TT. Only one case where there are 0 heads.

Probability of even number = 2/3

Combined probability = \frac{3}{4}* \frac{2}{3} = \frac{1}{2}
Option D
Manager
Joined: 14 Oct 2012
Posts: 116
Own Kudos [?]: 260 [0]
Given Kudos: 1023
A fair coin is to be tossed twice and an integer is to be [#permalink]
Hello Friends, I got this question correct by fluke.
What i did was this: P(2T & odd) = 1/2*1/2*1/3 = 1/12
P(atleast one T & odd) = 1-P(2T & odd) = 11/12 which isn't even the answer.
Can anyone explain me what am i doing wrong?
Can't we take both events together? If so how to do it?

Figured out what i was doing wrong: Here it goes for anyone who thought like me...
P(2T & odd) = P(2T)*P(odd) = (1/2*1/2)*(1/3)
but, P[(atleast 1 H)&(even)] = [(1- P(2 Tails) )&(1 - P(odd))] = [(1 - 1/4)*(1 - 1/3)] = [3/4 * 2/3] = 1/2

If you like it, kudo...
VP
Joined: 11 Aug 2020
Posts: 1246
Own Kudos [?]: 208 [1]
Given Kudos: 332
Re: A fair coin is to be tossed twice and an integer is to be [#permalink]
This is how I thought about it.

a) P(1 head + 1 even) = 1/2 x 2/3 = 1/3
b) P(2 heads + 1 even) = 1/2 x 1/2 x 2/3 = 1/6

P(1 head + 1 even) + P(2 heads + 1 even) = 1/3 + 1/6 = 1/2

Non-Human User
Joined: 09 Sep 2013
Posts: 34039
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: A fair coin is to be tossed twice and an integer is to be [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: A fair coin is to be tossed twice and an integer is to be [#permalink]
Moderator:
Math Expert
94430 posts