# 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:
111 comments Page 1 of 12.

Shobha said:   1 week 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.

Triveni said:   3 weeks ago

Amit Verma said:   3 months 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.
(9)

Tejeshwari said:   9 months ago
Thanks all for explaining it.
(2)

Zahid said:   1 year ago
How to find the events of coins quickly like TTT and HHT etc? explain me.
(1)

MUKESH MAHLI said:   2 years ago
At most mean- less than or less than equal to.

Am I right?

Dhivya said:   2 years ago
Thank you for explaining @Sundar.

Sumanth said:   3 years ago
It is 6/8=3/4.
(1)

Meena said:   3 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?
(2)

Neeraja said:   3 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?