Mathematics · Probability · NCERT Examples

Example 9

A complete, independently verified solution for NCERT Example 9.

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Mathematics · Chapter 14 · NCERT Examples

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NCERT Example

Example 9

two coins · at least one head

Harpreet tosses two different coins simultaneously. Find the probability that she gets at least one head.

Solution

Board-exam working:

Write H for head and T for tail. Because the coins are different, HT and TH are distinct outcomes.

S={HH,HT,TH,TT},n(S)=4S=\{HH,HT,TH,TT\},\qquad n(S)=4

The outcomes containing at least one head are HH, HT and TH.

E={HH,HT,TH},n(E)=3E=\{HH,HT,TH\},\qquad n(E)=3
P(E)=34P(E)=\frac34

The same result follows by subtracting the probability of no head.

P(E)=1−P(TT)=1−14=34P(E)=1-P(TT)=1-\frac14=\frac34

Final answer

P(at least one head)=34\boxed{P(\text{at least one head})=\frac34}

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