Letters of the word ‘EDUCATION’ are re-arranged. Find the pr

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 Multiple Choice QuestionsLong Answer Type

481.

On her vacations, Veena visits four cities (A, B, C and D) in a random order. What is the probability that she visits:

(i) A before B? (ii) A before B and B before C?

(iii) A first and B last? (iv) A either first or second (v) A just before B? 

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 Multiple Choice QuestionsShort Answer Type

482.

In a relay race, there are five teams, A, B, C, D and E.

What is the porbability

(i) that A, B, C finish first, second and third respectively?

(ii) that A, B and C are first three to finish (in any order)?

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484. Letters of the word ‘DELAYS’ are arranged. Find the probability that D and S are at the end places of the new word.
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485. 5 girls are arranged in a row. Find the probability that the youngest and the eldest are always together.
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486.

Letters of the word ‘EDUCATION’ are re-arranged. Find the probability that the vowels are always together.

Also, find the probability that the vowels are not all together.


Number of letters in the word ' EDUCATION' = 9
  Number of vowels = 5
Number of consonants = 4
Number of arrangements for 9 letters = 9!
rightwards double arrow                     n(S) = 9!
Event A: The vowels are always together
rightwards double arrow                       n(A) = r! (n - r + 1)!
where r = 5, n - r + 1 = 9 - 5 + 1 = 5
rightwards double arrow                        n(A) = space 5 factorial space cross times space 5 factorial

Hence,        straight P left parenthesis straight A right parenthesis space equals space fraction numerator straight n left parenthesis straight A right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction space equals space fraction numerator 5 factorial cross times 5 factorial over denominator 9 factorial end fraction equals fraction numerator 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator 9 cross times 8 cross times 7 cross times 6 end fraction equals 5 over 126

Also, the probability that not all the vowels are together
                straight P left parenthesis straight A with bar on top right parenthesis space equals space 1 minus straight P left parenthesis straight A right parenthesis space equals space 1 minus 5 over 126 equals 121 over 126

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 Multiple Choice QuestionsLong Answer Type

487. Which of the follwing ‘are’ and ‘are not’ probabilities of occurrence of an event A?
(i) straight P left parenthesis straight A right parenthesis equals 7 over 6                        (ii)  P(A) = 1                       (iii) P(A) = 0
(iv) straight P left parenthesis straight A right parenthesis equals fraction numerator negative 3 over denominator 2 end fraction                   (v) P(A) = space 2 over 5                     (vi) <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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#6 {main}</pre>
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 Multiple Choice QuestionsShort Answer Type

488. The probability that Mrs Shah will get a job in the bank is 3/7. What is the probability that she will not get the job?
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489. The probability that the hunter will miss the target is 2/3 . What is the probability that he will hit the target?
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490. One coin is tossed, find the probability of getting (i) a tail (ii) no tail.
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