Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 29 May 2017, 11:39

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If a fair coin is tossed 4 times, what's the probability

Author Message
TAGS:

### Hide Tags

Manager
Joined: 22 Nov 2003
Posts: 54
Location: New Orleans
Followers: 1

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

If a fair coin is tossed 4 times, what's the probability [#permalink]

### Show Tags

25 Nov 2003, 09:48
If a fair coin is tossed 4 times, what's the probability that at least 3 of the 4 tosses will come up heads?

This question is taken directly from a Kaplain guide I have. I know that I can use 2^4 to determine the total possibilities and I can likewise just manually list the number of tosses w/3 heads, but I want to understand the formula. Can someone help me understand this mathematically?

Thanks,
CJ
SVP
Joined: 03 Feb 2003
Posts: 1604
Followers: 9

Kudos [?]: 269 [0], given: 0

### Show Tags

26 Nov 2003, 03:41

4/16+1/16=5/16
Director
Joined: 28 Oct 2003
Posts: 501
Location: 55405
Followers: 1

Kudos [?]: 25 [0], given: 0

### Show Tags

26 Nov 2003, 07:34
Alternatively,

You can do the formula for exactly two heads, and divide the "remainder" by two...
Director
Joined: 14 Oct 2003
Posts: 583
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 53 [0], given: 0

### Show Tags

26 Nov 2003, 09:51
Here's another way of looking at it

No tails HHHH = 4C0 = 1
One Tail THHH = 4C1 = 4
TWO Tails TTHH = 4C2 = 6
Three Tails TTTH = 4C3 = 4
Four Tails TTTT = 4C4 = 1

Total number of desired cases = 5/
Total number of cases = 16

Thus 5/16
SVP
Joined: 14 Apr 2009
Posts: 2069
Location: New York, NY
Followers: 394

Kudos [?]: 1442 [0], given: 8

Re: If a fair coin is tossed 4 times, what's the probability [#permalink]

### Show Tags

24 Sep 2012, 09:30
At least 3 heads from 4 tosses.

We can use combination to figure out ways that we can pick 3 out of 4 to have heads

4C3

THen add 4C4 - out of 4, choose all four to have heads.

4C3 + 4C4 = total # combinations

2^4 = total # of variations.

Recall that when it comes to coin flipping, it's just one value. Either heads or tails. It's the same idea as in poker, you get one card value but it has 4 variations (hearts, spade, club, or diamond).

In poker, if you got dealt the same card 4 times, you would be looking at 4^4 variations. But with the coin, we only have 2 states (NOT 4 like in poker). So the variations is 2^4

(4C3 + 4C4) / 2^4
= (4 + 1) / 16
= 5/16
Re: If a fair coin is tossed 4 times, what's the probability   [#permalink] 24 Sep 2012, 09:30
Similar topics Replies Last post
Similar
Topics:
Probability - Why consider order while tossing a coin( or any event) ? 0 30 Jun 2016, 12:53
What is the probability of randomly selecting one of...... 4 16 Apr 2013, 00:51
5 Probability of deaths after 4 days 2 01 Apr 2013, 21:26
50 A bag contains 3 white balls, 3 black balls & 2 red balls 22 14 Apr 2017, 04:24
158 Set S consists of numbers 2, 3, 6, 48, and 164. Number K is 20 19 Aug 2016, 04:19
Display posts from previous: Sort by