Eleven dimes dated 1989 through 1999 are tossed. Find the probability of the event.
-Heads on the 1991 and 1997 dimes only
A) 19912048
B) 19972048
C) 10241
D) 20481

Question

Quizplus · Accepted Answer

The probability of getting heads on exactly two specific coins (1991 and 1997) and tails on the others out of eleven coins is calculated by recognizing that each coin has two possible outcomes (heads or tails). Thus, for the two coins that we want to land on heads, there are $2^2 = 4$ favorable outcomes (but since we want a specific outcome, it's actually just 1 favorable outcome for our specific case). For the remaining 9 coins, we want all of them to land on tails, which has $2^9 = 512$ possible outcomes in general, but again, we're looking for a specific outcome (all tails), so for our purpose, it's considered 1 outcome for these 9 coins. The total number of possible outcomes for tossing 11 coins is $2^{11} = 2048$. The probability of our specific event (heads on the 1991 and 1997 dimes only) is therefore 1 out of 2048, since there's only one way to achieve this specific outcome out of the 2048 possible outcomes when tossing 11 coins.

Eleven Dimes Dated 1989 Through 1999 Are Tossed