Alfie spun a spinner with three coloured sections 20 times and recorded some of his results in the table below. a) How many times did the spinner land on pink? b) Alfie spins the spinner again . Based on the experimental probabilities, which colour is it most likely to land on? c) Copy and complete the sentence below to explain how Alfie could improve his experiment to get better estimates for the probabilities. __ square square square square

This question is presented in a table with missing values which we should determine based on the available information. The contents of the table are:<br /><br />1. The spinner has three colors: Orange, Pink, and Black.<br />2. The frequencies for orange and pink are not provided. For black, it is given as 10. <br />3. The experimental probability for orange is given as 0.4 (as fraction, 0.4 = 2/5), but for pink and black, these are not provided.<br />4. There are some hints on ways to improve the experiment, yet most of them are unrelated to our calculations.<br /><br />Let's proceed to fill in the missing values:<br /><br />a) To find out how many times the spinner landed on Pink, assume this as 'P' as we don't have sufficient information to calculate it yet.<br /><br />b) The colour that spinner is most likely to land on is based on the highest probability or highest frequency. Right now calculating that isn't possible as some frequencies are unknown. <br /><br />We do, however, know the total number of spins, i.e., it is 20. Given black was spun 10 times and pink 'P' times, and orange was spun the remainder times with an associated probability of 2/5. Let's fill in the frequency of orange first:<br /><br />The probability of spinning an orange in 20 attempts is:<br />\[\ P ( \text { orange } ) = \frac { \text { Frequency of orange } } { \text { Total number of spins } }\]<br />\[\ \frac{2}{5} = \frac { \text { Frequency of orange } } { 20 }\]<br /><br />By cross multiplying, we get Frequency of orange = 2/5 * 20 = 8. <br /><br />Coming back to 'P'. If frequency of spinning Black is 10 and Orange is 8 in 20 spins, it becomes clear that the spins for Pink will be 'P' = [total spins - (Orange spins + Black spins)].<br /> <br />Substituting the values, \(P = 20 - (8 + 10) = 2\)<br /><br />So "# times the spinner landed on Pink" = 2.<br /><br />c) As for estimating probabilities better, Alfie could improve his experiment by increasing the total number of spins. Since probabilities extent towards their true value as the number of attempts increases, the more spins Alfie does, the better his probability estimates will be.<br /><br />After all the calculations, filling in the table, <br /><br />\begin{array}{|c|c|c|}<br\ />\hline\ Colour\ &\ Frequency\ &\ Experimental\ Probability\ \\<br\ />\hline\ <br\ />Orange\ &\ 8\ &\ 0.4\ \\<br\ />Pink\ &\ 2\ &\ 0.1\ \\<br\ />Black\ &\ 10\ &\ 0.5\ \\<br\ />\hline<br\ />\end{array}<br /><br />Hence:<br /><br />a) The spinner landed on pink 2 times.<br /> <br />b) Based on the experimental probabilities, the spinner most likely landed on black. <br /> <br />c) Alfie could improve his experiment and get better estimates for the probabilities by stably constructing and engaging in many more spins.