Directions at a fate, cards bearing numbers 1 to 1000 one number on one card are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square number greater than 500, the player wins a prize. What is the probability that the second player wins a prize, if the first has already won?

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0.008

0.0008

0.08

0.8

answer is A.

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Detailed Solution

Given, directions at a fate, cards bearing numbers 1 to 1000 one number on one card are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square number greater than 500, the player wins a prize.
The significance of probability is essentially the degree to which something is likely to occur.
This is the fundamental probability hypothesis, which is also used in probability appropriation, where you will become acquainted with the possibility of results for an arbitrary investigation.
To determine the likelihood of a single event occurring, we must first know the total number of possible outcomes.
Mention the total sample space total numbers in the sample space =1000
Consider the perfect square numbers between 500 and 1000.
Thus, the outcomes of the favourable events

= 232, 242, 252, 262, 272, 282, 292, 302, 312

Find the probability that the first player wins.

Probability = Number of favourable events Total number of possible events

Thus, the probability that a first player win

= 9991000

Find the probability of the second player winning.
The card is not replaced.
Thus, the total number of outcomes =999 given that the first player has won.
So, the number of favorable outcomes =8.
Thus, the probability of the second player wins

= 8999

=0.008
At a fate, cards bearing numbers 1 to 1000 and one number on one card are put in a box.
Each player selects one card at random and that card is not replaced.
If the selected card has a perfect square number greater than 500, the player wins a prize.
The probability that the second player wins a prize, if the first has already win is

8999

= 0.008.
Hence, the correct option is 1.

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