wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The experiment is to repeatedly toss a coin until first tail shows up. Identify the type of the sample space.

A
Finite sample space
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Continuous sample space
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Infinite discrete sample space
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C Infinite discrete sample space
The experiment is to repeatedly toss a coin until first tail shows up.
A coin is tossed. The possible outcomes are headH,tailT.
Look into the following table:

1st toss 2nd toss 3rd toss 4th toss5th toss
T

H T
H H T
H H H T
H H H H T
If we get T at first toss, then our experiment ends.
Otherwise second toss. If we get T, out experiment ends. If not the process continues till we end up in tail.
Hence the possible outcomes are sequences of H that, if finite, end with a single T, and an infinite sequence of H.
Therefore, S={T,HT,HHT,HHHT,HHHHT,...,{HHHH....}}
Thus we get a infinite but countable(depends on the number of toss) sample space.
As we shall see elsewhere, this is a remarkable space that contains a not impossible event whose probability is 0.
We know that, "a discrete sample space is one with a finite or countably infinite number of possible values."
Hence, it is a infinite discrete sample space.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Total Probability Theorem
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon