Problem Solving

BTGmoderatorDC wrote: ↑

Sun Apr 05, 2020 5:38 pm

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

OA E

Source: Magoosh

Given that the probability is 0.6 that an “unfair” coin will turn up tails on any given toss, the probability that it turns head = 1 – 0.6 = 0.4.

Let's calculate the probability that in none of the tosses, the coin turns tail.

=> probability = (0.4)*(0.4)*(0.4) = (2/5)^3

Thus, the probability that at least one of the tosses will turn up tails = 1 – (2/5)^3 = 117/125 = 0.936

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorDC wrote: ↑

Sun Apr 05, 2020 5:38 pm

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


OA 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

BTGmoderatorDC wrote: ↑

Sun Apr 05, 2020 5:38 pm

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


OA E

Source: Magoosh

Since the probability of obtaining tails on one toss is 0.6, then the probability of obtaining heads on one toss is 1 - 0.6 = 0.4.

We can use the formula:

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

P(no tails) = P(3 heads) = 0.4 x 0.4 x 0.4 = 0.064

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

Answer: E