Question

Neeta is playing a game of cards with her brother.
She puts some cards numbered from 10 to 81
in a bag and mixes them together. Neeta wins
if she draws a card that bears a number which
when divided by 5 gives a remainder of 2. The
probability that she loses the game is​

Answer 1

Answer: 82.72% chance of losing or in fraction 67/81 (81-14/81)

Step-by-step explanation: the numbers between 10 and 81, which when divided by 5 have a remainder of 2 are the ones which are two numbers more than numbers divisible by 5.

example: 27 (25+2).

so just add 2 to all the numbers which are divisible by 5, and those are the numbers that Neeta should pick to win the game.

so, 12,17,22,27,32,37,42,47,52,57,62,67,72,77 (14 cards).

the total number of cards she has is (81-10)+1=72.

the number of cards with numbers that when divided by 5 have remainder 2 is 14 (as seen in above).

so the possibility is 14/81 cards.

= 0.17283950617

change to percentage:

= 0.17283950617×100%

=17.28% (2 decimal places)

=17.28% chance of winning.

so the remaining is the chance to lose. (CHANCE TO LOSE=TOTAL CHANCES-CHANCES TO WIN)

100%-17.28%

=82.72% chance of losing or in fraction 67/81 (81-14/81)