# Aptitude - Probability - Discussion

Discussion Forum : Probability - General Questions (Q.No. 5)
5.
Three unbiased coins are tossed. What is the probability of getting at most two heads?
 3 4
 1 4
 3 8
 7 8
Explanation:

Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}

Let E = event of getting at most two heads.

Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.

 P(E) = n(E) = 7 . n(S) 8

Discussion:
119 comments Page 1 of 12.

Jiju said:   1 year ago
At most means maximum, that means no more than 2 heads, so the events include TTT, HTT, HHT, THH, TTH, HTH, and THT.

HHH is not right because it's more than two heads, at most means not more than two so it includes 0 heads, 1 head, 2 heads.
(39)

Amit Verma said:   1 year ago
Here S = {TTT, TTH, THT, THH, HHH, HHT, HTH, HTT}
Let E = Even of getting at most two heads.
Then E = {HHH, HHT, HTH, THH},
P(E) = n(E)/n(S),
= 4/8 = 1/2.
(36)

Asmi said:   11 months ago
At most means not more than 2 heads.

And at least means more than 2 heads.
(20)

Shobha said:   1 year ago
I don't understand this logic - Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
As this question says event of getting at most two heads.

It should be these combinations- THH, HTH, HHT, HHH.
(15)

Manisha Yadav said:   8 months ago
The right answer should be 3/8.
(14)

Meena said:   4 years ago
The question is what is the probability of getting "at most" two heads?

So, HHH is more than two heads. It is not counted in Event. Am I right?
(6)

Chelsia said:   8 months ago
We can get quickly the number of events like 2 to the Power of (number of coins).

I.e 2'3=> 8.
(6)

Neeraja said:   4 years ago
@ Vivek Rai.

A coin is tossed 3 times. We have 8 possible outcomes. In those 8 possible outcomes, we should choose the outcomes in which we have 1 head, 2 heads or no heads (3tails). But according to you if you consider the only head side of the coin then how did you get 8 in the denominator?

(5)

Zahid said:   2 years ago
How to find the events of coins quickly like TTT and HHT etc? explain me.
(5)

Reena said:   3 months ago
At most 2 heads means it cannot be more than 2. It can be zero or 1 or 2 but not 3. And there is only one case that have 3 (HHH). So probability is 7/8.
(5)