Matematick Forum - Recent Posts https://matematick.com/forums/ Matematick Discussion Board en-US Sat, 18 Apr 2026 07:49:40 +0000 wpForo 60 Answer to: Finding the probability that the die shows an odd number and the coin shows a head https://matematick.com/forums/probability/finding-the-probability-that-the-die-shows-an-odd-number-and-the-coin-shows-a-head/#post-338 Tue, 15 Jun 2021 14:31:51 +0000 \small S=\left \{ (1,H), (2,H), (3,H), (4,H),(5,H), (6,H), (1,T), (2,T), (3,T), (4,T), (5,T), (6,T) \right \}

Let E be the event "the die shows an odd number and the coin shows a head". Event E may be described as follows

\small E=\left \{ (1,H), (3,H), (5,H) \right \}

The probability P(E) is given by 

\small P(E)=n(E)/n(S)=3/12=1/4.

]]> Staff https://matematick.com/forums/probability/finding-the-probability-that-the-die-shows-an-odd-number-and-the-coin-shows-a-head/#post-338 Finding the probability that the die shows an odd number and the coin shows a head https://matematick.com/forums/probability/finding-the-probability-that-the-die-shows-an-odd-number-and-the-coin-shows-a-head/#post-337 Tue, 15 Jun 2021 14:31:45 +0000

A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the coin shows a head.

]]> Staff https://matematick.com/forums/probability/finding-the-probability-that-the-die-shows-an-odd-number-and-the-coin-shows-a-head/#post-337 Answer to: Finding the probability https://matematick.com/forums/probability/finding-the-probability/#post-336 Tue, 15 Jun 2021 14:31:25 +0000 Total number of balls = 8 + 7 + 6 = 21.

Let E= event that the ball drawn is neither red nor green

        = event that the ball drawn is blue

n(E)=7

\small P(E)=\frac{n(E)}{n(S)}=\frac{7}{21}=\frac{1}{3}.

]]> Staff https://matematick.com/forums/probability/finding-the-probability/#post-336 Finding the probability https://matematick.com/forums/probability/finding-the-probability/#post-335 Tue, 15 Jun 2021 14:31:09 +0000

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

]]> Staff https://matematick.com/forums/probability/finding-the-probability/#post-335 Answer to: Combination https://matematick.com/forums/combinatorics/combination-2/#post-334 Tue, 15 Jun 2021 14:30:48 +0000 The word 'LEADING' has 7 different letters. When the vowels EAI are always together, they can be supposed to form one letter. Then, we have to arrange the letters LNDG (EAI). Now, 5 (4 + 1 = 5) letters can be arranged in 5!=120 ways. The vowels (EAI) can be arranged among themselves in 3!=6 ways. Required number of ways = 120 x 6 = 720. 

]]> Staff https://matematick.com/forums/combinatorics/combination-2/#post-334 Combination https://matematick.com/forums/combinatorics/combination-2/#post-333 Tue, 15 Jun 2021 14:30:42 +0000

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

]]> Staff https://matematick.com/forums/combinatorics/combination-2/#post-333 Answer to: Combination https://matematick.com/forums/combinatorics/combination/#post-332 Tue, 15 Jun 2021 14:30:14 +0000 Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.

The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.

The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.

 Required number of numbers = (1 x 5 x 4) = 20.

]]> Staff https://matematick.com/forums/combinatorics/combination/#post-332 Combination https://matematick.com/forums/combinatorics/combination/#post-331 Tue, 15 Jun 2021 14:30:08 +0000 How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

]]> Staff https://matematick.com/forums/combinatorics/combination/#post-331 Answer to: Trigonometry triangles https://matematick.com/forums/triangles-diagonals/trigonometry-triangles-2/#post-330 Tue, 15 Jun 2021 14:29:25 +0000 Since a,b,c form a geometric sequence, then \small b^2=ac.  Applying the sine theorem, we have \small sin^2B=sinAsinC.  Then 

\small 1-cos(A-C)\Rightarrow 2cos^2B+cosB-1\geq 0\Rightarrow cosB\geq \frac{1}{2}, 

or    \small cosB\leq -1  (truncated).

Hence \small 0<B\leq \frac{\Pi }{3}.

Additionally since   \small sinB+cosB=\sqrt{2}sin(B+\frac{\Pi }{4})\Rightarrow 1\leq m^2\leq \sqrt{2}  

\small \Rightarrow -\sqrt{2}\leq m\leq -1,   or  \small 1\leq m\leq \sqrt{2}.

]]> Staff https://matematick.com/forums/triangles-diagonals/trigonometry-triangles-2/#post-330 Trigonometry triangles https://matematick.com/forums/triangles-diagonals/trigonometry-triangles-2/#post-329 Tue, 15 Jun 2021 14:28:57 +0000  pZ3Ty3HGgrWyMkOfGzy1MyBFhg9lVovF-soru-41-1.jpg

]]> Staff https://matematick.com/forums/triangles-diagonals/trigonometry-triangles-2/#post-329