Chapter 7
The Mathematics of Maybe: Introduction to Probability
CBSE Class 9
Mathematics Solutions
Educart Mathematics class Class 9 NCERT Exemplar cover
Question:

Can you calculate the probability of getting one head and one tail?                                      [Page No. 169]

Answer: Verified

When two coins are tossed, the sample space is S={HH,HT,TH,TT}S = \{HH, HT, TH, TT\} with four equally likely outcomes.
'One head and one tail' happens in two of these: HTHT (first coin head, second tail) and THTH (first coin tail, second head).
Both show exactly one head and one tail, so there are 22 favourable outcomes out of 44.

OutcomeDescription
HHtwo heads
HTone head and one tail (favourable)
THone head and one tail (favourable)
TTtwo tails

Therefore

P(one head and one tail)=favourable outcomestotal outcomesP(\text{one head and one tail}) = \frac{\text{favourable outcomes}}{\text{total outcomes}}

=24=12=0.5 or 50%.= \frac{2}{4} = \frac{1}{2} = 0.5 \text{ or } 50\%.

A common slip is to think there is only one way to get 'a head and a tail'. But HT and TH are different outcomes, they differ in which coin shows the head even though both have one head and one tail. That is why the probability is 12\frac{1}{2}, not 14\frac{1}{4}.

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