WEBVTT
00:00:00.679 --> 00:00:03.369
A box contains 56 balls.
00:00:03.959 --> 00:00:08.809
The probability of selecting at random a red ball is five-sevenths.
00:00:09.279 --> 00:00:12.159
How many balls in the box are not red?
00:00:13.439 --> 00:00:21.159
The event of selecting a red ball and the event of selecting a ball that is not red are complementary events.
00:00:21.749 --> 00:00:29.099
The probability of the complement of ๐ด, denoted ๐ด bar, is equal to one minus the probability of ๐ด.
00:00:30.249 --> 00:00:37.669
In this question, we are told that the probability of selecting a red ball, ๐ of ๐
, is equal to five-sevenths.
00:00:38.559 --> 00:00:45.159
This means that the probability of selecting a ball that is not red is one minus five-sevenths.
00:00:45.859 --> 00:00:48.339
This is equal to two-sevenths.
00:00:49.299 --> 00:00:55.469
The probability of an event occurring and its complement must always sum to one.
00:00:56.649 --> 00:01:01.629
We are also told in this question that there are 56 balls in the box.
00:01:02.329 --> 00:01:10.089
Two-sevenths of these 56 balls are not red, so we need to calculate two-sevenths of 56.
00:01:10.959 --> 00:01:18.269
As the word โofโ in mathematics means multiply, we need to multiply two-sevenths by 56.
00:01:19.029 --> 00:01:22.529
56 is the same as 56 over one.
00:01:23.459 --> 00:01:29.949
We can then cross cancel or cross simplify by dividing 56 and seven by seven.
00:01:30.839 --> 00:01:37.819
This gives us two over one multiplied by eight over one, which is equal to 16 over one.
00:01:38.189 --> 00:01:42.149
We multiply the numerators and denominators separately.
00:01:42.989 --> 00:01:51.379
As this is equal to 16, we can conclude that 16 of the 56 balls in the bag are not red.
00:01:52.619 --> 00:01:57.859
An alternative method here would be to calculate the number of red balls first.
00:01:58.729 --> 00:02:03.129
We can do this by working out five-sevenths of 56.
00:02:03.779 --> 00:02:08.379
This is equal to 40, so we have 40 red balls in the box.
00:02:09.239 --> 00:02:12.859
This means that the rest of the balls must not be red.
00:02:13.589 --> 00:02:17.269
56 minus 40 is equal to 16.
00:02:18.279 --> 00:02:23.599
This once again proves that there are 16 balls in the box that are not red.