Please answer this probability question!?

Question

Set C = {1,2,3,4,5}. if two distinct members of Set C are selected at random, and then the minute hand of a clock is moved to point at one of the members selected and the hour hand of this clock is moved to point at the other member selected, find the probability that the smaller angle formed by these two hands of the clock is acute. Express you answer as a common fraction reduced to lowest terms.

Answer 1

Which number gets the minute hand and which gets the hour hand doesn't matter here, so it's a combinations thing.

There are 5C2 = 10 different pairs of numbers that we can draw.

To get an acute angle, the two numbers picked must be less than 3 apart (a diff of 3 results in a right angle which is not acute). This excludes the pairs (1,4), (1,5) and (2,5). The 7 other pais will give us an acute angle.

So the probability is 7/10.

Answer 2

360/12 = 30 deg/number

So, there's 30 deg between consecutive numbers.

There are 5C2 (=5C3 = 5*4/2 = 10) ways to choose the two numbers

Acute means less than or equal to 90 deg, right? The equality makes a big difference here!


If the two numbers are 1 and 5, then the angle is obtuse. The probability of drawing those two numbers, without regard to order is 2/(5*4) = 1/10

any other numbers, the angle is acute. with prob = 1-1/10= 9/10.

*** But! ***
You must decide what happens with the 90 deg case. It will make a big difference.

I'll look tomorrow to see what you've done and then continue.

Answer 3

the most excellent way is to guage that, when you consider that there are 7 + 5 = 12 large marbles, and 5 of those are yellow, the prospect that a marble is yellow provided that it truly is large is 5/12. -- even with the undeniable fact that, you're maximum impressive that it truly is easily a kind of P(A|B) type questions ... those are common as "conditional possibility" questions. P(A|B) ability "the prospect of A, given B." we are requested the prospect that the marble is yellow, provided that it truly is large. So, let A = the shape that the marble is yellow, and let B = the shape that the marble is large. Then, we are requested to locate P(A|B). by the definition of conditional possibility, P(A|B) = P(A?B) / P(B) to that end, P(A?B) = the prospect that a marble is both yellow and massive. when you consider that there are 5 large, yellow marbles out of 20, P(A?B) = 5/20 = a million/4 P(B) is the prospect that a marble is large. when you consider that there are 7 large, purple marbles and 5 large, yellow marbles, the total type of massive marbles is: 7 + 5 = 12, out of 20. So, P(B) = 12/20 = 3/5. Substituting those values, P(A|B) = (a million/4) / (3/5) = 5/12