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Probability

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

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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

Here n = 6
p = Probability of head = $1 half comma space space straight q space equals space 1 space minus space straight p space equals space 1 minus 1 half space equals 1 half$
P (at least 4 heads) = P (4) + P (5) + P (6)
$equals space straight C presuperscript 6 subscript 4 space open parentheses 1 half close parentheses squared space open parentheses 1 half close parentheses to the power of 4 space plus space straight C presuperscript 6 subscript 5 space open parentheses 1 half close parentheses space open parentheses 1 half close parentheses to the power of 5 space plus space straight C presuperscript 6 subscript 6 space open parentheses 1 half close parentheses to the power of 6 equals space open parentheses 1 half close parentheses to the power of 6 space open square brackets straight C presuperscript 6 subscript 4 space plus straight C presuperscript 6 subscript 5 space plus space straight C presuperscript 6 subscript 6 space close square brackets space equals space 1 over 64 space open square brackets fraction numerator 6 space cross times 5 space over denominator 1 space cross times 2 end fraction space plus 6 over 1 plus 1 close square brackets space equals 1 over 64 open square brackets 15 plus 6 plus 1 close square brackets space equals 22 over 64 equals space 11 over 32$

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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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