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Probabilities are used to determine the chances of events
The value of t is 16
The number of bricks is given as t
Let the number of red bricks be x.
So, the number of blue bricks would be t - x
So, the probability values are:
[tex]\frac{x -1}{t - 1} = \frac 13[/tex] --- when the both bricks are red
[tex]\frac{x}{t - 1} = \frac 25[/tex] --- when only the second brick is red
Divide both equations
[tex]\frac{x -1}{t - 1} \div \frac{x}{t - 1} = \frac 13 \div \frac 25[/tex]
Divide
[tex]\frac{x -1}{x} = \frac 13 \div \frac 25[/tex]
This gives
[tex]\frac{x -1}{x} = \frac 13 *\frac 52[/tex]
Evaluate the product
[tex]\frac{x -1}{x} = \frac 56[/tex]
Cross multiply
[tex]6x - 6 = 5x[/tex]
Collect like terms
[tex]6x - 5x = 6[/tex]
[tex]x = 6[/tex]
Recall that:
[tex]\frac{x -1}{t - 1} = \frac 13[/tex]
So, we have:
[tex]\frac{6 -1}{t - 1} = \frac 13[/tex]
[tex]\frac{5}{t - 1} = \frac 13[/tex]
Cross multiply
[tex]t -1 =15[/tex]
Add 1 to both sides
[tex]t = 16[/tex]
Hence, the value of t is 16
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