# 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 2 of 12.

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)

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

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

MUKESH MAHLI said:   3 years ago
At most mean- less than or less than equal to.

Am I right?
(4)

Dhivya said:   3 years ago
Thank you for explaining @Sundar.

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

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)

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)

Vivek Rai said:   4 years ago
But it says heads that mean only head should be counted not the tail side of the coin as we know a coin has 2 side head and tail and the question is asking about at most 2 heads so it should be = 3/8.

(2)

Sriram said:   4 years ago
@sara.

We can get 2 heads any position out of 3 (- - -) each position has 1/2 probability. So, (1/2*1/2*1/2) + (1/2*1/2*1/2) + (1/2*1/2*1/2) =3/8.

Do the same way for 1 head (1 out of 3 positions) is (1/2*1/2*1/2) + (1/2*1/2*1/2) + (1/2*1/2*1/2) =3/8.

And last without a head is 1/8.

Add (atmost 2 to atlast 0) 1/8+3/8+3/8=7/8.