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In this question, we are given a two -digit code with the following.
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The first digit is a random integer from 0 to 5 inclusive, and the second digit is a random integer from 0 to 8 inclusive.
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We are given the event e is the first digit is even, f, the second digit is odd, and g, the product of the 2 digit is odd.
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Now let's do the sample space first.
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I have an excel here.
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Now over here column b here is the first number from 0 to 5.
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And row 3 here is the second number from 0 to 8.
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And over here is the product of the first number and a second number.
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I'm going to show you how to do this.
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So you can have the second number here.
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And over here you can have the first number.
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All right.
00:56
So for the first number, we will start from 0 ,1.
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I can select this 2 and pull it down vertically until you reach 5.
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And for the second number, 0, tap to the next cell, 0 1, highlight the 2 and drag it horizontally until you get 8.
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Alright.
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Now over here, so 8, 8, 8, 8, 8, 9.
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Alright, over here we're going to do the product.
01:30
So i'm just going to...
01:33
Okay, so for this cell will be 0 times 0.
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So you put it equal, highlight this cell, put a multiply sign, which is the asterisk, and highlight this cell, and we'll get this.
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Now, i have to fix my column b, so i put a dollar sign, and i have to fix my row three.
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And so just pull this along vertically and drag it down.
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Sorry, pull it along horizontally and drag it down vertically, and you will get this.
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Okay, so this is the product for the first number.
02:09
The second number.
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Okay, let's go back to the whiteboard.
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Now, in a, we want to find the number or come in f.
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Okay.
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Now, f means the second digit is odd, and g means the product is odd.
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So let's go back to a sample space here.
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Second digit is odd.
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I'm going to highlight my columnus press down the control key for all the odd number here, and the product is odd.
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So again, holding down my control key i'm going to select all the odd number in my product here.
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Now you can see that there are actually 12 of them...