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The probability is 0.6 that an “unfair” coin will turn up

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by BTGModeratorVI » Sun Feb 23, 2020 6:59 am

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Answers

A

B

C

D

E

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Difficulty—

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 one of the tosses will turn up tails?

A. 0.064
B. 0.36
C. 0.64
D. 0.784
E. 0.936

Answer: E
Source: Magoosh
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Re: The probability is 0.6 that an “unfair” coin will turn up

by Brent@GMATPrepNow » Tue Feb 25, 2020 7:39 am
BTGModeratorVI wrote: ↑
Sun Feb 23, 2020 6:59 am
 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 one of the tosses will turn up tails?

A. 0.064
B. 0.36
C. 0.64
D. 0.784
E. 0.936

Answer: E
Source: Magoosh
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
Brent Hanneson - Creator of GMATPrepNow.com
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Re: The probability is 0.6 that an “unfair” coin will turn up

by swerve » Tue Feb 25, 2020 4:10 pm
BTGModeratorVI wrote: ↑
Sun Feb 23, 2020 6:59 am
 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 one of the tosses will turn up tails?

A. 0.064
B. 0.36
C. 0.64
D. 0.784
E. 0.936

Answer: E
Source: Magoosh
Try as follows,

The probability that at least one of the tosses will turn up tails = 1 - the probability that all will be heads

\(= 1 - (0.4\cdot 0.4\cdot 0.4)\)
\(= 1 - 0.064\)
\(= 0.936\)

Where you went wrong:

Probability that 1 is tails = (.6*.4*.4)+(.4*.6*.4)+(.4*.4*.6)

Similarly for the probability that 2 is tails.. consider all the cases.

In your solution, you have considered only one case each for both of the above.

Even if you had solved it correctly, this method is longer and more complicated.. solve it as shown in my post above.. easier and quicker.

Regards!
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Re: The probability is 0.6 that an “unfair” coin will turn up

by Scott@TargetTestPrep » Fri Feb 28, 2020 7:45 am
BTGModeratorVI wrote: ↑
Sun Feb 23, 2020 6:59 am
 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 one of the tosses will turn up tails?

A. 0.064
B. 0.36
C. 0.64
D. 0.784
E. 0.936

Answer: E
Source: Magoosh
We can use the formula:

P(At least 1 tail) = 1 - P(no tails)

P(no tails) = 0.4 x 0.4 x 0.4 = 0.064

P(at least 1 tail) = 1 - 0.064 = 0.936

Answer: E

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