# 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?

Answer: Option

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:

120 comments Page 1 of 12.
Sundar said:
1 decade ago

Hi Guys,

At most two heads means "Total number of HEADs can be 0 to 2".

So we cannot include HHH, because it contains 3 heads.

But we can include TTT, because ZERO head is accepted.

Therefore, the given answers is perfectively correct.

You may ask your doubts here if you have regarding this question?

Have a nice day!

At most two heads means "Total number of HEADs can be 0 to 2".

So we cannot include HHH, because it contains 3 heads.

But we can include TTT, because ZERO head is accepted.

Therefore, the given answers is perfectively correct.

You may ask your doubts here if you have regarding this question?

Have a nice day!

(1)

Malarvizhi said:
1 decade ago

How did say n(s) is 8?

Sundar said:
1 decade ago

@Malarvizhi

Note: "At most two heads" --(means)--> Not more than two heads.

Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} <--- (8 combinations)

Therefore, n(S) = 8.

Note: "At most two heads" --(means)--> Not more than two heads.

Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} <--- (8 combinations)

Therefore, n(S) = 8.

Abhijit said:
1 decade ago

Total no of probabilities= 2^3 =8

for 2/1/0 heads probability is =7(only 1 left HHH)

for 2/1/0 heads probability is =7(only 1 left HHH)

Dharini said:
1 decade ago

I cant follow what abhijit said why it is 2 power 3?

Murugesh said:
1 decade ago

@dharini...

2---> H & T

3---> total no of coins.

so 2^3.

2---> H & T

3---> total no of coins.

so 2^3.

Dinesh said:
1 decade ago

Got it murugesh

thanks..

thanks..

SATHYA said:
1 decade ago

What is unbiased coins?

Sathish said:
1 decade ago

Thank you sundar.

Sara said:
1 decade ago

Won't it be 3 out of 8?

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