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  • The probability that out of 10 persons, all born in April, at least two have the same birthday isOption: 1 <img alt="\mathrm{\frac{{ }^{30} C_{10}}{(

The probability that out of 10 persons, all born in April, at least two have the same birthday is

Option: 1

\mathrm{\frac{{ }^{30} C_{10}}{(30)^{10}}}


Option: 2

\mathrm{1-\frac{{ }^{30} C_{10}}{30 !}}


Option: 3

\mathrm{\frac{(30)^{10}-{ }^{30} C_{10}}{(30)^{10}}}


Option: 4

None of these


Answers (1)

best_answer

There are 30 days in April.

\mathrm{n(S)}= the number of ways in which 10 persons can have birthdays in the month of April

=30 \times 30 \times \ldots \text { to } 10 \text { times }=30^{10}

                                           (because each person can have birthday in 30 ways).

\mathrm{n(E)}=\mathrm{n(S)}- the number of ways in which 10 persons can have different birthdays

     \begin{aligned} & \mathrm{=30^{10}-{ }^{30} C_{10}} . \\ \\\therefore \: \: \: & \mathrm{P(E)=\frac{30^{10}-{ }^{30} C_{10}}{30^{10}}} . \end{aligned}

 

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Ritika Jonwal

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