Probability qs

Take Your Pants Off

I cant seem to get qs 3/4/5 I know were supposed to use bernoulis trial but how come with different probabilities.

MathsManiac

Use the following rules:

If A and B are independent events, then the probability that A and B both happens the probability that A happens multiplied by the probability that B happens.

If A and B are 'mutually exclusive'* events, the probability that A or B happens is the the probability that A happens plus the probability that B happens.

*'mutually exclusive' means the two things cannot both happen. E.g., winning exactly one contract and winning exactly two contracts are mutually exclusive events. (Both of those things can't happen.) Winning the first contract and winning the second contract are not mutually exclusive. (Both of those things could happen.)

Take Your Pants Off

MathsManiac wrote: »

Use the following rules:

If A and B are independent events, then the probability that A and B both happens the probability that A happens multiplied by the probability that B happens.

If A and B are 'mutually exclusive'* events, the probability that A or B happens is the the probability that A happens plus the probability that B happens.

*'mutually exclusive' means the two things cannot both happen. E.g., winning exactly one contract and winning exactly two contracts are mutually exclusive events. (Both of those things can't happen.) Winning the first contract and winning the second contract are not mutually exclusive. (Both of those things could happen.)

But are we using bernoulli's trials?
Thanks

LLMMLL

Take Your Pants Off wrote: »

But are we using bernoulli's trials?
Thanks

Bernoulli trials Are multiple trials of the same event right? So they always have the same probability of success or failure. These are 3 independent events.

I would work out the probability of success and failure for each of the 3 contracts (prob of success is given and prob of failure is 1- prob of success).

Then make an 8 row table of the possible outcomes where column 1 is success or failure of event 1 etc.

So:

SSS for getting all 3 contracts
SSF for getting the first 2
SFF for getting the first
SFS for getting the first and 3rd
.
.
.
FFF for getting no contracts

Work out probability of each of those rows by MULTIPLYING the relevant probabilities. Then work out the probability of the overall event asked for by ADDING the relevant rows.

So for example the probability of getting at least one contract is gotten by adding up every row that has at least one S (which should be the same as 1- FFF)

Take Your Pants Off

Thank you so much guys.
Really well explained, understand it now !