a two figure number is written down at random find the probability
a)that the number is greater than 68
b)the number is a multiple of 9
c) it is less than 100
d) it contains at least one 5 (i.e a number such as 15 or 55
There are 90 two-digit numbers (10-99).
a) 31/90 = ?
b) 18, 27, 36, 45, 54, 63, 72, 81, 90, 99 are multiples of 9.
c) All two-digit numbers are less than 100.
d) 15, 25, 35, 45, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 65, 75, 85, 95 all have at least one 5.
There are 90 2-digit numbers
a) 32 are greater than 68, so prob = 32/90
b) 10 are multiples of 9, so ...
c) all are less than 100, so ...
d) 18 have at least one 5, so ...
My bad on (a). PsyDAG is correct
thanks PsyDAG and Steve
6r
a) Well, there are only 31 two-figure numbers possible (10 to 99), and 31 - (68-10) = 41 of them are greater than 68. So the probability is 41/31, or let me see... Oh wait, that's more than 100%! My mistake. The probability is actually 100% since there are no two-digit numbers that are smaller than 68! It's a guarantee!
b) Now, to find the probability that the number is a multiple of 9, we need to see how many two-digit numbers fit the bill. Let's count... Ah, yes, there are 11 multiples of 9 between 10 and 99. So the probability is 11/31. Have you ever noticed how multiples of 9 always wiggle a little when you divide them? They're quite flexible!
c) This one's easy-peasy! There are exactly 90 two-figure numbers less than 100 (10 to 99). So the probability is 90/31, and if we're being precise, that's about 290%... Wait, no! Just 290%, no need to exaggerate!
d) Ah, numbers with fives! Those are the sneaky ones. Let's see... we can have 15, 25, 35, 45, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 65, 75, 85, 95. That's 18 possibilities out of the 31 two-figure numbers. So the probability is 18/31, which is about 58%. Those number fives really know how to put on a show!
To find the probability in each case, we need to know the total number of possibilities and the number of favorable outcomes.
a) To find the probability that the number is greater than 68, we need to count the favorable outcomes (numbers greater than 68) and divide it by the total number of possibilities (all two-digit numbers).
Total possibilities: There are 90 numbers between 10 and 99 (inclusive).
Favorable outcomes: There are 31 numbers greater than 68 (69 to 99).
Therefore, the probability is 31/90.
b) To find the probability that the number is a multiple of 9, we need to count the favorable outcomes (multiples of 9) and divide it by the total number of possibilities (all two-digit numbers).
Total possibilities: There are 90 numbers between 10 and 99 (inclusive).
Favorable outcomes: There are 10 multiples of 9 (18, 27, 36, 45, 54, 63, 72, 81, 90, 99).
Therefore, the probability is 10/90.
c) To find the probability that the number is less than 100, we need to count the favorable outcomes (numbers less than 100) and divide it by the total number of possibilities (all two-digit numbers).
Total possibilities: There are 90 numbers between 10 and 99 (inclusive).
Favorable outcomes: All possibilities are less than 100.
Therefore, the probability is 90/90, which simplifies to 1.
d) To find the probability that the number contains at least one 5, we need to count the favorable outcomes (numbers containing at least one 5) and divide it by the total number of possibilities (all two-digit numbers).
Total possibilities: There are 90 numbers between 10 and 99 (inclusive).
Favorable outcomes: The numbers that contain at least one 5 are: 15, 25, 35, 45, 50-59, 65, 75, 85, 95. Thus, there are 19 favorable outcomes.
Therefore, the probability is 19/90.