GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The probability is 0.6 that an “unfair” coin will turn up ta
[#permalink]
14 Mar 2019, 09:45
14 Mar 2019, 09:45
Expert Reply
1
Bookmarks
00:00
Question Stats:
68% (01:07) correct
31% (01:14) wrong based on 98 sessions
Hide Show timer Statistics
The probability is 0.6 that an “unfair” coin will turn up tails on any given toss. If the coin is tossed 3 times, what is the probability that at least 1 of the tosses will turn up tails?
A. 0.064
B. 0.36
C. 0.64
D. 0.784
E. 0.936
A. 0.064
B. 0.36
C. 0.64
D. 0.784
E. 0.936
Re: The probability is 0.6 that an “unfair” coin will turn up ta
[#permalink]
20 Mar 2019, 15:27
20 Mar 2019, 15:27
3
Expert Reply
If at least 1 of the tosses is tails, then 1, 2, or all 3 tosses could be tails. The only possibility this leaves out is the possibility of no tails at all, or all three tosses being heads. So we can simply calculate that probability and subtract it from 1.
The probability of the first toss being heads is 0.4. The probability of the second toss being heads is also 0.4. Same for the third as well. Together, the probability of heads on the first AND second AND third tosses is \(0.4*0.4*0.4 = 0.064\) (generally speaking, in probability "and" means multiply).
So, the probability of this one specific case, all heads, not happening is \(1 - 0.064 = 0.936\).
The probability of the first toss being heads is 0.4. The probability of the second toss being heads is also 0.4. Same for the third as well. Together, the probability of heads on the first AND second AND third tosses is \(0.4*0.4*0.4 = 0.064\) (generally speaking, in probability "and" means multiply).
So, the probability of this one specific case, all heads, not happening is \(1 - 0.064 = 0.936\).
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: The probability is 0.6 that an “unfair” coin will turn up ta
[#permalink]
15 Jan 2020, 06:52
15 Jan 2020, 06:52
2
Carcass wrote:
The probability is 0.6 that an “unfair” coin will turn up tails on any given toss. If the coin is tossed 3 times, what is the probability that at least 1 of the tosses will turn up tails?
A. 0.064
B. 0.36
C. 0.64
D. 0.784
E. 0.936
A. 0.064
B. 0.36
C. 0.64
D. 0.784
E. 0.936
ASIDE---------------
We want P(select at least 1 tails)
When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(getting at least 1 tails) = 1 - P(not getting at least 1 tails)
What does it mean to not get at least 1 tails? It means getting zero tails.
So, we can write: P(getting at least 1 tails) = 1 - P(getting zero tails)
-------------------
P(getting zero tails)
P(getting zero tails) = P(heads on 1st toss AND heads on 2nd toss AND heads on 3rd toss)
= P(heads on 1st toss) x P(heads on 2nd toss) x P(heads on 3rd toss)
= 0.4 x 0.4 x 0.4
= 0.064
So, P(getting at least 1 tails) = 1 - 0.064 = 0.936
Answer: E
Cheers,
Brent
