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प्रश्न
Let X represent the difference between the number of heads and the number of tails when a coin is tossed 6 times. What are the possible values of X?
उत्तर
A coin is tossed 6 times and X represents the difference between the number of heads and the number of tails.
Sample space of the experiment is
S = {(0 heads, 6 tails), (1 head, 5 tails), (2 heads, 4 tails), (3 heads, 3 tails), (4 heads, 2 tails), (5 heads, 1 tail), (6 heads, 0 tails)}
The values of X corresponding to these outcomes are as follows:
∴ X(0 heads, 6 tails) = 0 – 6 = – 6
X(1 head, 5 tails) = 1 – 5 = – 4
X(2 heads, 4 tails) = 2 – 4 = – 2
X(3 heads, 3 tails) = 3 – 3 = 0
X(4 heads, 2 tails) = 4 – 2 = 2
X(5 heads, 1 tail) = 5 – 1 = 4
X(6 heads, 0 tails) = 6 – 0 = 6
∴ Possible values of X are {– 6, – 4, –2, 0, 2, 4, 6}.
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