Video: Pack 1 • Paper 2 • Question 4

Pack 1 • Paper 2 • Question 4

01:58

Video Transcript

The set of colours on a biased spinner is red, orange, yellow, green, indigo, and violet. The table below shows the probabilities that the spinner will land on each colour. Billy spins the spinner 300 times. Work out an estimate for the total number of times the spinner will land on blue or orange.

Notice how the table is currently incomplete. Before we can answer this question, we first need to find the value of the missing probability. Remember, the sum of the probabilities for all possible outcomes of an event, here the colours the spinner might land on, is one. If we, therefore, subtract the given probabilities from one, we get that the probability the spinner will land on blue to be 0.08.

When two events are mutually exclusive, this means they can’t happen at the same time. The probability that either one or the other will occur is the sum of the probability of each event. Here the probability the spinner will land on orange or blue is equal to the probability the spinner will land on orange plus the probability the spinner will land on blue. The probability is, therefore, 0.23 add 0.08, which is equal to 0.31.

Finally, we need to work out an estimate for the number of times the spinner will land on orange or blue. 0.31 is the probability of one counter chosen at random being orange or blue. We, therefore, multiply this probability by 300 to figure out how many times we will expect it to land on orange or blue. 300 multiplied by 0.31 is equal to 93. We will expect it to land on orange or blue 93 times.

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