If `Aa n dB` each toss three coins. The probability that both get the same number of heads is `1//9` b. `3//16` c. `5//16` d. `3//8`
If `Aa n dB`
each toss three coins. The probability that both get the same number of
heads is
`1//9`
b. `3//16`
c. `5//16`
d. `3//8`
A. `1//9`
B. `3//16`
C. `5//16`
D. `3//8`
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Correct Answer - C
The proablitty that A gets r heads in three tosses of a coin is
`P(X=r)=""^(3)C_(r)((1)/(2))^(r)((1)/(2))^(3-r)=""^(3)C_(r)((1)/(2))^(3)`
The probability that A and B both get r heads in three tosses of a coin is
`""^(3)C_(r)((1)/(2))^(3)""^(3)C_(r)((1)/(2))^(3)=(""^(3)C_(r))^(2)((1)/(2))^(6)`
Hence, the required probability is
`underset(r=0)overset(3)sum(""^(3)C_(r))((1)/(2))^(6)=((1)/(2))^(6){1+9+9+1}=(20)/(64)=5/16`
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