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Probability

Short Answer Type

471. Two cards are drawn simultaneously from a pack of 52 well shuffled cards. Find the probability that both cards are red.

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472. Two cards are drawn simultaneously from a pack of 52 well shuffled cards. Find the probability that one card is red and one is black.

Two cards are drawn simultaneously from a pack of 52 cards.
Number of equally likely, exhaustive outcomes = n(S) = $straight C presuperscript 52 subscript 2 equals space fraction numerator 52 factorial over denominator 2 factorial space 50 factorial end fraction equals fraction numerator 52 cross times 51 over denominator 2 cross times 1 end fraction equals 26 cross times 51$
Event A: One card is red and one is black.
$rightwards double arrow$ Favourable elements = (26 red, 1 to draw; 26 black, 1 to draw)
$rightwards double arrow$ $straight n left parenthesis straight A right parenthesis equals straight C presuperscript 26 subscript 1 times straight C presuperscript 26 subscript 1 space equals space 26 cross times 26$
P(A) = Probability that one card is red and one card is black
$equals fraction numerator straight n left parenthesis straight A right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals fraction numerator 26 cross times 26 over denominator 26 cross times 51 end fraction equals 26 over 51$

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473. In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket.

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474. In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy two tickets.

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475. In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy ten tickets.

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476.

In a lottery, there are 35 tickets in all, 10 bearing prize numbers and 25 are blanks. A lady draws 2 tickets at random. What is the probability that she will win one prize.

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477. In a lottery, there are 35 tickets in all, 10 bearing prize numbers and 25 are blanks. A lady draws 2 tickets at random. What is the probability that she will win two prizes?

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478. In a lottery, there are 35 tickets in all, 10 bearing prize numbers and 25 are blanks. A lady draws 2 tickets at random. What is the probability that she will win no prize?

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Long Answer Type

479.

A bag contains 3 red balls bearing numbers 1, 2, 3 (one number on one ball) ; and two black balls bearing numbers 4 and 6. A ball is drawn, its number noted and the ball is replaced in the bag. Then another ball is drawn and its number noted. Find the probability of drawing:

(i) 2 on the first draw and 6 on the second draw.

(ii) a number ≤ 2 on the first draw and 4 on the second draw.

(iii) a total of 5.

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Short Answer Type

480. The number lock of a suitcase has 4 wheels, each labelled with 10 digits i.e., from 0 to 9. The lock opens with a sequence of 4 digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

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