Suppose the odds against winning the lottery are \( 45,000,000 \) to 1 . What is the probability of the event of winning the lottery given these odds? \( \mathrm{P}(\mathrm{E})=\square \) (Type an integer or a simplified fraction.)

To determine the probability of winning the lottery given the odds against winning are \( 45,000,000 \) to 1, we can use the following reasoning: **Understanding Odds:** - **Odds Against**: This represents the ratio of unfavorable outcomes to favorable outcomes. In this case, there are \( 45,000,000 \) unfavorable outcomes (not winning) for every 1 favorable outcome (winning). **Calculating Probability:** The probability \( \mathrm{P}(\mathrm{E}) \) of an event \( \mathrm{E} \) occurring is given by: \[ \mathrm{P}(\mathrm{E}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} \] Given the odds against winning are \( 45,000,000 \) to 1: - **Number of Favorable Outcomes**: 1 (winning) - **Number of Unfavorable Outcomes**: \( 45,000,000 \) (not winning) - **Total Number of Possible Outcomes**: \( 45,000,000 + 1 = 45,000,001 \) Therefore: \[ \mathrm{P}(\mathrm{E}) = \frac{1}{45,000,001} \] **Answer:** \[ \mathrm{P}(\mathrm{E}) = \frac{1}{45,\!000,\!001} \]