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Probability

Long Answer Type

1071. If a fair coin is tossed 10 times, find the probability of
(i) exactly six heads
(ii) at least six heads
(iii) at most six heads

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1072. A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is

1 over 100.

What is the probaility that he will win a prize exactly once (a) at least once (b) exactly once (c) at least twice?

94 Views

1073.

An urn contains 25 balls of which 10 balls bear a mark ‘X’ and the remaining 15 bear a mark ‘Y’ . A ball is drawn at random and it is replaced. If 6 balls are drawn in this way, find the probability that
(i) all will bear mark X
(ii) not more than 2 balls will bear 'Y' mark.
(iii) at least one ball will bear 'Y' mark.
(iv) the number of balls with 'X' mark and 'Y' mark will be equal.

104 Views

Short Answer Type

1074. In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’ ; if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.

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1075. Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?

Here n = 10
$straight p space equals 90 over 100 space equals 9 over 10 comma space space space straight q space equals space 1 space minus space straight p space equals space 1 minus space 9 over 10 space equals space 1 over 10$
Required probability $equals space space straight P left parenthesis straight X space less or equal than space 6 right parenthesis$
$equals space 1 minus straight P left parenthesis 7 space less or equal than straight X less or equal than 10 right parenthesis space equals space 1 minus space sum from straight r space equals space 7 to 10 of space space straight C presuperscript 10 subscript straight r space open parentheses 1 over 10 close parentheses to the power of 10 minus straight r end exponent space open parentheses 9 over 10 close parentheses to the power of straight r$

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1076. How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?

139 Views

Multiple Choice Questions

1077. In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is

$10 to the power of negative 1 end exponent$
$open parentheses 1 half close parentheses to the power of 5$
$open parentheses 9 over 10 close parentheses to the power of 5$
$open parentheses 9 over 10 close parentheses to the power of 5$

114 Views

1078. The probability that a student is not a swimmer is

1 fifth.

Then the probability that out of five students, four are swimmers is

$straight C presuperscript 5 subscript 4 space open parentheses 4 over 5 close parentheses to the power of 4 space 1 fifth$
$open parentheses 4 over 5 close parentheses to the power of 4 space 1 fifth$
$straight C presuperscript 5 subscript 1 space open parentheses 4 over 5 close parentheses to the power of 4$
$straight C presuperscript 5 subscript 1 space open parentheses 4 over 5 close parentheses to the power of 4$

87 Views

Long Answer Type

1079. A and B throw two dice simultaneously turn by turn. A will win if he throws a total of 5, B will win if he throws a doublet. Find the probability that B will win the game, though A started the game.

176 Views

Short Answer Type

1080.

A bag X contains 4 white balls and 2 black balls, while another bag Y contains 3 white balls and 3 black balls. Two balls are drawn (without replacement) at random from one of the bags and were found to be one white and one black. Find the probability that the balls were drawn from bag Y.

1714 Views