Of the 1,000 students in a local college, 420 own brand X mobile phones and 580 own brand Y mobile phones. Of these students, 80 own both brands of mobile phones. Find the probability that a student chosen at random has a brand X mobile phone given that he has a brand Y mobile phone.
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Have you learned conditional probability?
Do you know how to draw the Venn diagram of the situation?
To draw the Venn diagram, you subtract 80 (own both) from 420 who own phone X to get 340 students who own ONLY phone x. Similarly for y.
X=event that a student owns phone X, and
Y=event that a student owns phone Y.
So out of the 1000 students, we have 80 who own both, so P(X\(\cap\)Y)=80/1000.
conditional probability that the student owns X given that he owns Y is, by definition of conditional probability
Since all quantities on the right-hand side are known, the required probability can be calculated.
Thanks so much ! Can you help me with another ?
Definitely, if you participate!
in a factory the chance that a certain machine works without overheating in the morning is 50% . if it runs smoothly all morning then there is an 85% chance that it will continue for the rest of the day and 15% chance that it will stop due to over heating . what is the probability that on a given gay it will work in the morning and overheat later on ?
& my bad I'm doing this Plato thing
Here's a tree diagram that I started. Can you please fill in the probabilities of each branch?
Its 7.5% ?
Did you get that without using the tree diagram?
I did sum extra stuff & it seemed right . & it was correct !! Any idea ab this one ? Two friends, Bob and Ben, each buy one lottery ticket. Each ticket contains six numbers from a total of one hundred numbers (0–99). Bob chooses the numbers 1, 2, 3, 4, 5, 6, and Ben chooses the numbers 39, 45, 66, 72, 74, 89. Who has a higher probability of winning?
What do you think?
I think Ben just not sure
and your reasoning?
Bc his numbers are kinda scattered so he has a better number choices
You know in these lotteries, they use identical physical balls each with a number painted on it. This is to make sure every number has an equal chance of being drawn.
So based on this information, can you reconsider your reasoning?