In summer 2015, as happens most summers in the UK, a question from the GCSE Mathematics paper (for 16-year-olds) made it into the press for being “impossible”. 299 more words

## Tags » Probability

#### A man speaks the truth 3 out of 4 times. He throws a die and reports it to be a 6. What is the probability of it being a 6?

As with every conditional probability problem, first thing is to mark the events:

Let event **A** be the man reports 6, and event… 146 more words

#### Law of total probability

The law expresses the total probability of an outcome which can be realized via several distinct events. It says that if is a finite or countably infinite partition of a sample space (in other words, a set of pairwise disjoint events whose union is the entire sample space) then for any event… 7 more words

#### If a coin is tossed twice, is the event of two heads is more likely if we know that the first toss is a head, or if we know that at least one of the tosses is a head.

This is another one of those probability questions with answers that appear to be counterintuitive. The first thought is, of course, that in both cases the information is the same – one of the toss was a head – so the probabilities should be the same. 177 more words

#### Suppose you're given the choice of three doors: Behind one door is a prize; behind the others, nothing. You pick a door, and the host, who knows what's behind the doors, opens another door, which has nothing behind it. Is it to your advantage to switch your choice?

This is a very popular question, and you will find a solution pretty much anywhere where people are talking about quant interviews. Unfortunately, most of the times, although the given solution is correct, the explanation is either not very clear or plain wrong. 536 more words

#### There are 1000 coins in a bag. One of them has heads on both sides. You pick a coin and, without looking at it, flip it ten times. And every time you get a head. What is the probability that this is the bad coin.

If we define an event that the coin is bad as **B**, and the event that any coin flipped ten times produces 10 heads as… 95 more words

#### The 7 Things to Check When to Grasp a Probability Distribution

- The random variable
- Check whether the variable discrete or continuous

- The probability (Mass/Density) Function
- The cumulative distribution function
- The expectation
- The variance
- The standard deviation… 15 more words