### Video Transcript

The table below contains data from
a survey of core gamers who were asked whether their preferred gaming platform was
the smartphone, the console, or the PC. The gamers are split by gender. Find the probability that a core
gamer chosen at random prefers using a console. Give your answer to three decimal
places. Given that a core gamer prefers to
play using a console, find the probability that they are male. Give your answer to three decimal
places.

Now, firstly, we recall that if
we’re trying to find the probability of an event occurring, we divide the number of
ways that event can occur by the total number of outcomes. And the first part of this question
asks us to find the probability that a gamer chosen at random prefers to use a
console. Now, they don’t specify whether
we’re interested in male or female gamers. So, in fact, we’re going to
calculate the totals.

We begin by calculating the total
number of gamers who prefer to use a smartphone. That’s 52 plus 48, which is
100. Similarly, to calculate the total
number of gamers who preferred the console, we add 37 and 23, to give us 60. Finally, the total number of gamers
who prefer to use the PC is 48 plus 35, which is 83. The total number of gamers
questioned is found by adding all of the values in this column. That’s 100 plus 60 plus 83, which
is 243.

Now, remember, we’re looking to
find the probability that the gamer chosen at random prefers to use a console. So that’s this second row. The total number of outcomes or the
total number of gamers here we calculated to be 243. So the probability that a core
gamer chosen at random prefers to use a console is 60 divided by 243, which is
0.2469 and so on. That’s 0.247.

The second part of this question
states that given that a core gamer prefers to play using a console, find the
probability that they are male. This phrase “given that” is an
indication that we’re going to use conditional probability. If we let event A be the event that
the gamer chosen is male and event B be the event that they prefer to use a console,
we use the bar notation to show that we’re trying to find the probability of A
occurring given that B has occurred. And what this does is narrow down
the data somewhat.

We’re told that the gamer prefers
to play using a console. So we can narrow our data down into
just those people who prefer to play using a console. And we want to find the probability
that they are male. So we’re going to divide the number
of male gamers who said they preferred using a console by the total number of gamers
who said they preferred using a console. That’s 37 divided by 60. That’s 0.61666 and so on, which
correct to three decimal places is 0.617. So the probability that a core
gamer is male given that they prefer to play using a console is 0.617.