Answer:
see the attached picture
A number is selected, at random, from the set {1,2,3,4,5,6,7,8}.
1 answer:
Applying the formula, you have:
A = the number is prime
B = the number is odd
I assume that with "random" you imply that all numbers can be chosen with the same probability. So, we have
because 4 out of 8 numbers are prime: 2, 3, 5 and 7.
Similarly, we have
because 4 out of 8 numbers are odd: 1, 3, 5 and 7.
Finally,
because 3 out of 8 numbers are prime and odd: 3, 5 and 7.
So, applying the formula, we have
Note:
I think that it is important to have a clear understanding of what's happening from a conceptual point of you: conditional probability simply changes the space you're working with: you are not asking "what is the probability that a random number, taken from 1 to 8, is prime?"
Rather, you are adding a bit of information, because you are asking "what is the probability that a random number, taken from 1 to 8, is prime, knowing that it's odd?"
So, we're not working anymore with the space {1,2,3,4,5,6,7,8}, but rather with {1,3,5,7} (we already know that our number is odd).
Out of these 4 odd numbers, 3 are primes. This is why the probability of picking a prime number among the odd numbers in {1,2,3,4,5,6,7,8} is 3/4: they are literally 3 out of 4.
You might be interested in
So, he's got 8 gallons of paint, to paint the two rooms, of the two rooms, one is twice as big as the other
now, "x" is how many gallons to paint the larger room with only one coat, however, the larger room uses 2 coats, so, the larger room uses 2x of paint
now, the client declined to paint the smaller one
so hmmm as I read... well, we dunno how many coats will go to the smaller room for one, we know the larger will use 2 coats, or 2x.. if we assume the smaller room was going to use say 1 coat or 1/2x
then one can say the painter bought enough for both rooms, 1coat for the small one and 2coats for the larger one
so, the paint the larger room, you'll 2x of paint, for 2coatsand to paint the smaller room, you'll need 1/2 x, because x gallons is how much is needed for the larger room, but the larger room is twice as big, thus the smaller room uses 1/2 of that in gallons
thus, with those assumptions, that the small room will use only 1 coat
that's who many gallons are needed for 1 coat in the larger roomrecall "x" is 1coat for the larger room
now, the client decides to skip the smaller roomso, the painter will only need 2x gallons then
he bought 8 gallons, 8 - 6.4, he's got left 1.6 gallons
now, "x" is how many gallons to paint the larger room with only one coat, however, the larger room uses 2 coats, so, the larger room uses 2x of paint
now, the client declined to paint the smaller one
so hmmm as I read... well, we dunno how many coats will go to the smaller room for one, we know the larger will use 2 coats, or 2x.. if we assume the smaller room was going to use say 1 coat or 1/2x
then one can say the painter bought enough for both rooms, 1coat for the small one and 2coats for the larger one
so, the paint the larger room, you'll 2x of paint, for 2coatsand to paint the smaller room, you'll need 1/2 x, because x gallons is how much is needed for the larger room, but the larger room is twice as big, thus the smaller room uses 1/2 of that in gallons
thus, with those assumptions, that the small room will use only 1 coat
that's who many gallons are needed for 1 coat in the larger roomrecall "x" is 1coat for the larger room
now, the client decides to skip the smaller roomso, the painter will only need 2x gallons then
he bought 8 gallons, 8 - 6.4, he's got left 1.6 gallons