Question

you pick a card at random. 2 3 4 5 6 7 what is p(greater than 4 or divisor of 50)? simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Identify total number of cards

There are 6 cards in total, so the total number of possible outcomes $n(S)=6$.

Step2: List numbers greater than 4

The numbers greater than 4 are 5, 6, 7. So $A = \{5,6,7\}$ and $n(A)=3$.

Step3: List divisors of 50

The divisors of 50 are 1, 2, 5, 10, 25, 50. Among the given cards, the divisors of 50 are 2, 5. So $B=\{2,5\}$ and $n(B) = 2$.

Step4: Find intersection of A and B

$A\cap B=\{5\}$, so $n(A\cap B)=1$.

Step5: Use addition - rule of probability

The formula for $P(A\cup B)$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Since $P(A)=\frac{n(A)}{n(S)}$, $P(B)=\frac{n(B)}{n(S)}$ and $P(A\cap B)=\frac{n(A\cap B)}{n(S)}$, we have $P(A\cup B)=\frac{n(A)+n(B)-n(A\cap B)}{n(S)}$. Substitute $n(A) = 3$, $n(B)=2$, $n(A\cap B)=1$ and $n(S)=6$ into the formula: $\frac{3 + 2-1}{6}=\frac{4}{6}=\frac{2}{3}$.

Answer:

$\frac{2}{3}$