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.