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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

106 Views

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.

148 Views

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?

89 Views

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.

Given,
Bag X =4 white, 2 black

Bag Y=3 white, 3 black

Let A be the event of selecting one white and one black ball.

E₁ = first bag selected

E₂ = second bag selected

$straight P left parenthesis straight E subscript 1 right parenthesis space equals 1 half space straight P left parenthesis straight E subscript 2 right parenthesis space equals 1 half straight P left parenthesis straight A over straight E subscript 1 right parenthesis space equals space 4 over 6 space straight x space 2 over 5 space plus space 2 over 6 space straight x 4 over 5 space equals 16 over 30 straight P open parentheses straight A over straight E subscript 2 close parentheses space equals space space 3 over 6 space straight x 3 over 5 space plus 3 over 6 space straight x 3 over 5 space equals 18 over 30 straight P open parentheses straight E subscript 2 over straight A close parentheses space equals space fraction numerator straight P space left parenthesis straight E subscript 2 right parenthesis straight P space left parenthesis straight A divided by straight E subscript 2 right parenthesis over denominator straight P left parenthesis straight E subscript 1 right parenthesis straight P left parenthesis straight A divided by straight E subscript 1 right parenthesis plus straight P left parenthesis straight E subscript 2 right parenthesis straight P left parenthesis straight A divided by straight E subscript 2 right parenthesis end fraction straight P open parentheses straight E subscript 2 over straight A close parentheses space equals space fraction numerator begin display style 1 half end style space straight x begin display style 18 over 30 end style over denominator begin display style 1 half end style space straight x begin display style 16 over 30 end style space plus begin display style 1 half end style space straight x begin display style 18 over 30 end style end fraction space equals fraction numerator 18 over denominator 16 plus 18 end fraction space space equals 18 over 34 space space equals 9 over 17$