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1051. A coin is tossed 5 times. What is the probability of getting
(i) at least 3 heads (ii) at most 2 heads

Here n = 5, p = P(getting head) = $1 half$ , q = 1 - p = 1 - $1 half space equals space 1 half$
(i) P(at least 3 heads) = P(3) + P(4) + P(5)
$equals space straight C presuperscript 5 subscript 3 space open parentheses 1 half close parentheses squared space open parentheses 1 half close parentheses cubed space plus space straight C presuperscript 5 subscript 4 space open parentheses 1 half close parentheses space open parentheses 1 half close parentheses to the power of 4 plus space straight C presuperscript 5 subscript 5 space open parentheses 1 half close parentheses to the power of 5 equals space open parentheses 1 half close parentheses to the power of 5 space open square brackets straight C presuperscript 5 subscript 3 space plus space straight C presuperscript 5 subscript 4 space plus space straight C presuperscript 5 subscript 5 close square brackets space equals space 1 over 32 space open square brackets fraction numerator 5 space cross times space 4 over denominator 1 space cross times 2 end fraction plus 5 over 1 plus 1 close square brackets equals space 1 over 32 left parenthesis 10 plus 5 plus 1 right parenthesis space equals space 16 over 32 space equals space 1 half$
(ii) P(at most 2 heads) = $1 minus open square brackets straight P left parenthesis 3 right parenthesis space plus space straight P left parenthesis 4 right parenthesis space plus space straight P left parenthesis 5 right parenthesis close square brackets space equals space 1 minus 1 half$

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Long Answer Type

1052. A pair of dice is thrown 6 times. If getting a total of 8 is considered a success, what is the probability of
(i) at least 4 successes?
(ii) at most 5 succcesses?

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Short Answer Type

1053. An unbiased coin is tossed six times. Find the probability of obtaining exactly 4 heads.

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1054. An unbiased coin is tossed six times. Find the probability of obtaining less than 3 heads .

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1055. An unbiased coin is tossed six times. Find the probability of obtaining more than 4 heads.

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1056. An unbiased coin is tossed six times. Find the probability of obtaining more than 4 heads and less than 6 heads.

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1057. An unbiased coin is tossed six times. Find the probability of obtaining more than 6 heads.

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1058. An unbiased coin is tossed six times. Find the probability of obtaining at least 4 heads

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1059. An unbiased coin is tossed six times. Find the probability of obtaining at most 4 heads.

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1060. An unbiased coin is tossed six times. Find the probability of obtaining 2 heads.

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Previous Year Papers

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Short Answer Type

1051. A coin is tossed 5 times. What is the probability of getting(i) at least 3 heads (ii) at most 2 heads

Long Answer Type

Short Answer Type

1051. A coin is tossed 5 times. What is the probability of getting
(i) at least 3 heads (ii) at most 2 heads