Four whole number taken at random are multiplied together. The chance that the…
2024
Four whole number taken at random are multiplied together. The chance that the last digit of the product is 1, 3, 7, or 9 is ?
- A.
14/625
- B.
16/625
- C.
15/625
- D.
12/625
Attempted by 16 students.
Show answer & explanation
Correct answer: B
Key idea: the last digit of the product is one of 1, 3, 7, or 9 exactly when each factor's last digit is one of 1, 3, 7, or 9 (these are the units modulo 10). If any factor has last digit 0, 2, 4, 5, 6, or 8, the product cannot end in 1, 3, 7, or 9.
Probability a random whole number ends in 1, 3, 7, or 9 = 4/10 = 2/5.
All four numbers must have such a last digit, and the choices are independent, so the probability = (2/5)^4.
Compute (2/5)^4 = 16/625.
Final answer: 16/625