SAT Subject Test Mathematics Level 2

If  the probability that    one event   will    occur   is  a   and the independent probability that    another

event   will    occur   is  b,  then    the probability that    both    events  will    occur   is  ab.

First, establish the sequence of events. Here you have two tosses of dice:

Toss    1 Toss  2

Second, write out the different ways in which what you want to occur could occur. For example, to
yield a product of at least 25, the dice could land showing a five (5) and a six (6). Note this and all the
other ways of getting at least 25:

Toss    1 Toss  2

One way: 5 5

Another way: 5 6

Another way: 6 5

Another way: 6 6

Third, replace each number with its simple independent probability. In other words, think of a
single, simple toss of one die. What’s the probability of getting 5? One in six—so replace every 5 with

. And on a single toss of a die, what’s the probability of getting 6? Again, one in six—so replace
every 6 with :

Toss    1 Toss  2

One way:

Another way:

Another way:

Another way:

Finally, because the probability of an event that could occur in more than one way is simply the sum
of the probabilities of the various ways in which the event could occur, multiply across and add