Video: Conditional Probability from a Two-Way Table

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.

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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.

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