Questions: Find the probability of the indicated event if P(E)=0.20 and P(F)=0.45. Find P(E or F) if P(E and F)=0.15. P(E or F)= (Simplify your answer.)

Find the probability of the indicated event if P(E)=0.20 and P(F)=0.45. Find P(E or F) if P(E and F)=0.15. P(E or F)= (Simplify your answer.)
Transcript text: Find the probability of the indicated event if $\mathrm{P}(\mathrm{E})=0.20$ and $\mathrm{P}(\mathrm{F})=0.45$. Find $P(E$ or $F)$ if $P(E$ and $F)=0.15$. $P(E$ or $F)=$ $\square$ (Simplify your answer.)
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Solution

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Solution Steps

Given:
  • $P(E) = 0.2$
  • $P(F) = 0.45$
  • $P(E \text{ and } F) = 0.15$
Step 1: Use the addition rule for probabilities to find $P(E \text{ or } F)$
  • $P(E \text{ or } F) = P(E) + P(F) - P(E \text{ and } F)$
  • $P(E \text{ or } F) = 0.2 + 0.45 - 0.15 = 0.5$

Final Answer:

  • $P(E \text{ or } F) = 0.5$
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