A fair coin is tossed 10 times and the outcomes are listed. Let $H i$ be the event that the $i th$ outcome is a head and $A m$ be the event that the list contains exactly m heads, then

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H 2 and A 5

are independent

A 1 and A 9

are independent

H 3 and A 4

are independent

A 1 and H 7

are independent

answer is C.

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Detailed Solution

$PH i = 12, PA m = 10 C m 210$
$PH i ∩ A m = 9 C m − 1 210$ for $H i and A m$
$\begin{array}{l} \frac{^{9} C_{m - 1}}{2^{10}} = \frac{1}{2} \cdot \frac{^{10} C_{m}}{2^{10}} \\ m = 5 \end{array}$

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A fair coin is tossed 10 times and the outcomes are listed. Let H i be the event that the i th outcome is a head and A m be the event that the list contains exactly m heads, then

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A fair coin is tossed 10 times and the outcomes are listed. Let $H i$ be the event that the $i th$ outcome is a head and $A m$ be the event that the list contains exactly m heads, then