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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.

112 Views

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.

Number of tickets = 10,000
Number of prizes bearing tickets = 10
Number of tickets bought = 1
Event A: The one ticket is a prize bearing ticket.
$rightwards double arrow$    $space space space space straight n left parenthesis straight S right parenthesis space equals space straight C presuperscript 10 comma 000 end presuperscript subscript 1$
   $straight n left parenthesis straight A right parenthesis equals straight C presuperscript 10 subscript 1$
∴    $straight P left parenthesis straight A right parenthesis equals fraction numerator straight n left parenthesis straight A right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals fraction numerator straight C presuperscript 10 subscript 1 over denominator straight C presuperscript 10000 subscript 1 end fraction equals 10 over 10000 equals 1 over 1000$
$rightwards double arrow$    $space space straight P left parenthesis straight A with bar on top right parenthesis space equals space 1 minus 1 over 1000 equals 999 over 1000$

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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.

120 Views

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.

131 Views

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?

98 Views

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.

189 Views

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?

127 Views