In a collection of tentickets, there are two winning tickets. From this collection, five tickets are

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14.Probability

hard

In a collection of tentickets, there are two winning tickets. From this collection, five tickets are drawn at random Let $p_1$ and $p_2$ be the probabilities of obtaining one and two winning tickets, respectively. Then $p_1+p_2$ lies in the interval

$\left(0, \frac{1}{2}\right]$

$\left(\frac{1}{2}, \frac{3}{4}\right]$

$\left(\frac{3}{4}, 1\right]$

$\left(1, \frac{3}{2}\right]$

(KVPY-2021)

Solution

(c)

$p _1=\frac{{ }^2 C _1 \cdot{ }^8 C _4}{{ }^{10} C _5}=\frac{2 \times 8 \times 7 \times 6 \times 5}{24 \times \frac{10 \times 9 \times 8 \times 7 \times 6}{120}}=\frac{5}{9}$

$p _2=\frac{{ }^2 C _2 \cdot{ }^8 C _3}{{ }^{10} C _5}=\frac{8 \times 7 \times 6}{6 \times \frac{10 \times 9 \times 8 \times 7 \times 6}{120}}=\frac{2}{9}$

$p _1+ p _2=\frac{7}{9}$

Standard 11

Mathematics

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easy

In a collection of tentickets, there are two winning tickets. From this collection, five tickets are drawn at random Let $p_1$ and $p_2$ be the probabilities of obtaining one and two winning tickets, respectively. Then $p_1+p_2$ lies in the interval

Solution

Similar Questions

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