A spinner is divided into
Note: You may use the following fact
from probability theory: If the probability of event
Solution 1
Let
Since
Solution 2
Let
If Jamal lands on red in at least one spin, then he may land red on the first spin only, red on the second spin only, or red on both spins.
If Jamal lands on red on his first spin only, then his second spin
must land on yellow. Since the results of each spin do not depend on
each other, the probability that he spins red on his first spin and
yellow on his second spin is
If Jamal lands on red on his second spin only, then his first spin
must land on yellow. Thus, the probability Jamal spins yellow on his
first spin and red on his second spin is
The probability that Jamal lands on red on his first spin and again
on his second spin is
The probability of getting at least one red in the two spins is equal
to the probability that he lands red on his first spin only, plus the
probability that he lands red on his second spin only, plus the
probability that he lands red on both spins. That is,
Since the spinner has only
Solution 3
Let
If Jamal lands on red in at least one spin, then the first red occurs on his first spin or on his second spin.
If Jamal lands on the first red on his first spin, then on his first
spin he spins a red, and on his second spin he spins any colour. Since the
results of each spin do not depend on each other, the probability that
the first red occurs on his first spin is
If Jamal lands on the first red on the second spin, then on his first
spin he spins a yellow, and on his second spin he spins a red. The
probability of this is
The probability of spinning at least one red on the two spins is
equal to the probability that he lands the first red on his first spin,
plus the probability that he lands the first red on his second spin.
That is,
Using the quadratic formula, we find