B) Consider an experiment of selecting two balls from a box...

b) Consider an experiment of selecting two balls from a box containing 10 balls numbered from 1 to 10. Assume that each ball is equally likely to be selected. What are the probabilities for the following events? i. The sum of the numbers on the two selected balls is 7. ii. The sum of the numbers on the two selected balls is 7 or 11. iii. The sum of the numbers on the two selected balls is greater than 3.

Transcript

0:00 Hello.

00:02 In this question we are given that a pair of two dice is being rolled.

00:10 Okay and we need to calculate what is the probability that sum is greater than 10.

00:14 Okay, for a pair of dice, following observation will be made 1 -2 -1 -3 and so on, up to 1 -6 and similarly in this direction 2 -1 -2 and so on and so on.

00:30 So for a sum to be more than 10, what are our favorable cases? okay, our favorable cases would be 5 .6, 6 .5 and 6 .6.

00:45 Okay, these are our favorable cases.

00:48 In all other cases, the sum would be less than or equal to 10.

00:52 So total number of cases would be 6 times 6.

00:56 That would be 36.

00:57 So our probability such that some is more than 10, it would be 3 over 36.

01:10 That would be 1 over 12.

01:12 This would be our answer to the first part of the first question.

01:17 And then we are asked in the second part that what is the probability that at least one die shows an odd number.

01:28 Okay, so for showing an odd number on either die, there can be four cases.

01:36 The first case is both will show odd.

01:41 Second is one will say odd, another will say even and third is even odd and the fourth case is owed on both.

01:53 Okay, so if we will, sorry, this is even and even.

02:01 Correct it is even and even and now what do we need to calculate? we need to calculate the probability that at least one die shows an odd number.

02:14 So only this case would be eliminated.

02:17 So 1 minus priority of showing an even is 1 by 2 and 2 probability of showing even on another die is 1 by 2.

02:27 So it would be 3 by 4.

02:30 There are 3 by 4 chances that it is would so at least one at least an owed on one night okay so for the next question sorry a bowl contains five red balls and six yellow balls okay you are randomly selecting the balls without replacement each ball is equally likely to be picked okay without replacement okay if two balls are picked from the ball what is the probability that both of them will be yellow.

03:07 Okay, so there are two bowls, there is one bowl in which there are five red and seven yellow.

03:18 Is it correct? let me check six yellow, sorry, there are six yellow balls...

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