Questions: Suppose that events E and F are independent, P(E)=0.6, and P(F)=0.7. What is the P(E and F) ? The probability P(E and F) is (Type an integer or a decimal.)

Transcript text: Suppose that events $E$ and $F$ are independent, $P(E)=0.6$, and $P(F)=0.7$. What is the $P(E$ and $F)$ ? The probability $\mathrm{P}(\mathrm{E}$ and F$)$ is $\square$ (Type an integer or a decimal.)

Solution

Solution Steps

To find the probability of two independent events $E$ and $F$ occurring together, we can use the formula for the intersection of independent events: $P(E \text{ and } F) = P(E) \times P(F)$. Given $P(E) = 0.6$ and $P(F) = 0.7$, we can calculate $P(E \text{ and } F)$ by multiplying these probabilities.

Step 1: Given Probabilities

We are given the probabilities of two independent events: \[ P(E) = 0.6 \] \[ P(F) = 0.7 \]

Step 2: Calculate the Probability of Both Events

Since events $E$ and $F$ are independent, the probability of both events occurring together is given by the formula: \[ P(E \text{ and } F) = P(E) \times P(F) \]

Step 3: Substitute the Values

Substituting the given probabilities into the formula: \[ P(E \text{ and } F) = 0.6 \times 0.7 \]

Step 4: Perform the Calculation

Calculating the product: \[ P(E \text{ and } F) = 0.42 \]