Question

multiplication rule for independent events
nick decides to play \spin to win\ at a fundraiser event. he has a 25% chance of winning on any individual spin. individual spins are independent. nick decides to play the game 10 times.
what is the probability that nick wins at least once?
round to 2 decimal places.

Explanation:

Step1: Find probability of losing once

The probability of winning a single spin is \( p = 0.25 \), so the probability of losing a single spin is \( q = 1 - p = 1 - 0.25 = 0.75 \).

Step2: Find probability of losing all 10 times

Since the spins are independent, the probability of losing all 10 times is \( q^{10} = 0.75^{10} \). Calculate \( 0.75^{10} \approx 0.0563 \).

Step3: Find probability of winning at least once

The probability of winning at least once is the complement of losing all 10 times. So, \( P(\text{win at least once}) = 1 - P(\text{lose all 10 times}) = 1 - 0.0563 = 0.9437 \).

Step4: Round to 2 decimal places

Rounding \( 0.9437 \) to two decimal places gives \( 0.94 \).

Answer:

\( 0.94 \)