Hi! Need help, I don’t understand the question
What is the greatest value of the function y = 4-2cosx?
Hi! The question is asking how high the curve gets at the peak of its oscillation. So the \(y=4\) part of the equation shifts the curve upwards to oscillate about \(y=4\), and the function will go 2 above and 2 below that (since it is \(2\cos{x}\). 2 above 4 is 6, so \(y=6\) is the greatest value of the function
how do you do this?
If 4 dice are thrown, find the probability that the dice will have
(a) four 6’s
(b) only one 6 (c) at least one 6.
Hi! So the trick with these is to
always draw tree diagrams. Like, anytime you get a probability question, try drawing a tree diagram as the default response. It will help you visualise the problem on top of helping you calculate the answer itself.
For Part (a), each dice has a probability of \(\frac{1}{6}\) of being a six. So the probability of all four being a six:
=\left(\frac{1}{6}\right)^4)
For (b), the tree diagram comes in handy. You'll see four branches, each with three \(\frac{5}{6}\) and one \(\frac{1}{6}\), but in different orders. Either way, the answer is:
=\frac{1}{6}\times\left(\frac{5}{6}\right)^3)
For Part C, we go to the complementary event. This is usually the case when we see
at least in the question. In this case, the opposite of having
at least one six is having no sixes. So, calculate the probability of no sixes then subtract that from 1 (or 100%, same thing). This is easier than individually counting every possible way to get at least one six.
=1-P\left(\text{No Sixes}\right)=1-\left(\frac{5}{6}\right)^4)
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