An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events :
A : the sum is greater then 8.
B : 2 occurs on either die
C : the sum is at least 7 and a multiple of 3.
Which pairs of these events are mutually exclusive ?

Two dice are thrown and the sum of the number which come up on the dice is noted. Let us consider the following events associated with the experiment A: 'the sum is even'. B: 'the sum is a multiple of 3'. C: 'the sum is less than 4'. D: 'the sum is greater than 11'. Which pairs of these events are mutually exclusive?

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment A : 'the sum is even' B : 'the sum is a multiple of 3'. C: 'the sum is less than 4' D: 'the sum is greater than 11'. Which pairs of these events are mutually exclusive ?

A die is throw. Describe the following events : A: The number on die is less than 7. B: The number on die is multiple of 3. C : The number on die is greater than 4. D: The number on die is smaller than 2. Also find AnnC,BuuC,D'uuC' .

Two dice are thrown write the sample space for this experiment. Describe the following events. Event A : The sum of the number on the dice is divisible by 4. Event B : The sum of the numbers on the dice is divisible by 3. Event C: The sum of the numbers is less than 7. Event D: Both the numbers on the dice are even.

A bag contains a red ball, a black ball, a yellow ball and a white ball. One ball is selected randomly and note its colour and then put it into the bag. Again second ball is selected and note its colour. Write the sample space for this experiment. Hence, describe the following events : (1) A: Selected both the balls are of same colours. (2) B: Only one ball is white. (3) C: At least one ball is white. (4) D: Both the balls are of different colour. Hence, find AnnB,BuuC,AuuD,AnnD . What can we say about the events B and C ? What can we say about the events A and D?

A pair of unbiased dice are rolled together till a sum of either 5 or 7 is obtained. Then find the probability that 5 comes before 7.

Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probabilityof the event 'the coin shows a tail', given that at least one die shows a 3'.

A die is thrown. Describe the following events : (i) A: a number less then 7 (ii) B : a number greater then 7 (iii) C: a multiple of 3. (iv) D : a number less then 4 (v) E : an even number greater then 4 (vi) F : a number not less then 3 Also find AuuB,AnnB,BuuC,EnnF,DnnE,A-C,D-E,EnnF',F' .

Thin films, including soap bubbles and oil slicks, show patterns of alternating dark and bright regions resulting from interference among the reflected light waves. If two waves are in phase their crest and troughs will coincide. The interference will be constructive and the aplitude of the resultant wave will be greater than the amplitude of either constituent wave. if the two waves are out of phase, the crests of one wave will coincide with the troughs of the other wave. The interference will be destructive and the amplitude of the resultant wave will be less than that of either constituent wave. at the interface between two transparent media some light is reflected and some light is refracted. * When incident light, reaches the surface at point a, some of the light is reflected as ray R_(a) and and some is refracted following the path ab to the back of the film. *At point b some of the light is refracted out of the film and part is reflected back refracted out of the fiml as ray R_(c) . R_(a) and R_(c) are parallel. However, R_(c) has travelled the extra distance within the film of abc. if the angle of incidence is small then abc is approximately twice the film's thickness. if R_(a) and R_(c) are in phase they will undergo constructive interference and the region ac will be bright if R_(a) and R_(c) are out of phase, they will undergo destructive interference. * Refraction at an interface never changes the phase of the wave. * For reflection at the interface between two media 1 and 2, if n_(1)ltn_(2) the reflected wave will change phase by pi . if n_(1)gtn_(2) the reflected wave will not undergo a phase change. for reference n_(air)=1.00 * if the waves are in phase after refection at all interfaces, then the effects of path length in the film are Constructive interference occur when (n= refractive index) 2t=mlamda//n" "m=0,1,2,3... .. Destructive interference occurs when 2t=(m+1//2)lamda//n" "m=0,1,2,3... Q. A 600 nm light is perpendicularly incident on a soap film suspended in air. The film is 1.00 mum thick with n=1.35. Which statement most accurately describes the interference of the light reflected by the two surfaces of the film?